## Discrete Subgroups of Semisimple Lie Groups

## On Some Aspects of the Theory of Anosov Systems

Uses ergodic theoretic techniques to study the distribution of periodic orbits of Anosov flows. The thesis introduces the "Margulis measure" and uses it to obtain a precise asymptotic formula for counting periodic orbits.

## Ergodic Theory And Fractal Geometry

## Instantons and Four-Manifolds

This book exposes the beautiful confluence of deep techniques and ideas from mathematical physics and the topological study of the differentiable structure of compact four-dimensional manifolds, compact spaces locally modeled on the world in which we live and operate.

## Surveys in Differential Geometry, Vol. 4: Integrable Systems

The survey volumes serve as continuing references, inspirations for new research, and introductions to the variety of topics of interest to differential geometers.

## Geometry and Quantum Field Theory

Exploring topics from classical and quantum mechanics and field theory, this book is based on lectures presented in the Graduate Summer School at the Regional Geometry Institute in Park City, Utah, in 1991.

## Geometry, Topology and Physics

Proceedings of the First Brazil-USA Workshop held in Campinas, Brazil, June 30-July 7, 1996

## Global Analysis in Modern Mathematics

## On the Functional Equations Satisfied by Eisenstein Series

## Base Change for GL(2)

R. Langlands shows, in analogy with Artin's original treatment of one-dimensional p, that at least for tetrahedral p, L(s, p) is equal to the L-function L(s, π) attached to a cuspdidal automorphic representation of the group GL(2, /A), /A being the adéle ring of the field, and L(s, π), whose definition is ultimately due to Hecke, is known to be entire.

## Euler products

James K. Whittemore lectures in mathematics given at Yale University

## Wavelets: Calderón-Zygmund and Multilinear Operators

The classic exposition of the theory of wavelets from two of the subject's leading experts. This volume discusses the theory of paradifferential operators and the Cauchy kernel on Lipschitz curves with the emphasis firmly on their connection with wavelet bases.

## Wavelets and Operators

The strength of wavelet methods lies in their ability to describe local phenomena more accurately than a traditional expansion in sines and cosines can. Thus, wavelets are ideal in many fields where an approach to transient behaviour is needed, for example, in considering acoustic or seismic signals, or in image processing.

## Oscillating Patterns in Image Processing and Nonlinear Evolution

Image compression, the Navier-Stokes equations, and detection of gravitational waves are three seemingly unrelated scientific problems that, remarkably, can be studied from one perspective.

## Wavelets, Vibrations and Scalings

Physicists and mathematicians are intensely studying fractal sets of fractal curves. Mandelbrot advocated modeling of real-life signals by fractal or multifractal functions. One example is fractional Brownian motion, where large-scale behavior is related to a corresponding infrared divergence. Self-similarities and scaling laws play a key role in this new area. There is a widely accepted belief that wavelet analysis should provide the best available tool to unveil such scaling laws.

## Algebraic Numbers and Harmonic Analysis

## Lectures on Differential Equations and Differential Geometry

This book is superbly written by a world-leading expert on partial differential equations and differential geometry. It consists of two parts. Part I covers the existence and uniqueness of solutions of elliptic differential equations. It is direct, to the point, moves smoothly and quickly, and there are no unnecessary discussions or digressions.

## Functional Analysis: Lectures Given at New York University, Courant Institute of Mathematical Sciences

## Topics in Nonlinear Functional Analysis

## Lectures on Linear Partial Differential Equations

## A Celebration of John F. Nash Jr.

This collection celebrates the pathbreaking work in game theory and mathematics of John F. Nash Jr., winner of the 1994 Nobel Prize in Economics. Nash’s analysis of equilibria in the theory of non-cooperative games has had a major impact on modern economic theory.

## Perspectives in Nonlinear Partial Differential Equations: In Honor of Haim Brezis

## Pseudo-differential Operators: Lectures given at a Summer School of the Centro Internazionale Matematico Estivo

## On Nonlinear Elliptic Partial Differential Equations and Holder Continuity

## Techniques in Linear and Nonlinear Partial Differential Equations

## Collected Papers of Mitio Nagumo

Especially among Japanese mathematicians Mitio Nagumo (1905-1995) is regarded as one of the greatest pioneers in research on differential equations. However, so far most of his papers have only been published in Japanese journals and were unavailable in the West.

## Open Problems in Mathematics

This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias.

## Theory of Probability and Random Processes

A one-year course in probability theory and the theory of random processes, taught at Princeton University to undergraduate and graduate students, forms the core of this book. It provides a comprehensive and self-contained exposition of classical probability theory and the theory of random processes. The book includes detailed discussion of Lebesgue integration, Markov chains, random walks, laws of large numbers, limit theorems, and their relation to Renormalization Group theory.

## Probability Theory: An Introductory Course

Sinai's book leads the student through the standard material for ProbabilityTheory, with stops along the way for interesting topics such as statistical mechanics, not usually included in a book for beginners.

## Topics in Ergodic Theory

This book concerns areas of ergodic theory that are now being intensively developed. The topics include entropy theory (with emphasis on dynamical systems with multi-dimensional time), elements of the renormalization group method in the theory of dynamical systems, splitting of separatrices, and some problems related to the theory of hyperbolic dynamical systems.

## Selecta I: Ergodic Theory and Dynamical Systems

The first volume is devoted to ergodic theory and dynamical systems. It contains 19 papers divided into four groups.

## Selecta II: Probability Theory, Statistical Mechanics, Mathematical Physics and Mathematical Fluid Dynamics

The 20 papers contained in this volume span the areas of mathematical physics, dynamical systems, and probability.

## Selecta III: Professor Sinai's Selected Papers

## Russian Mathematicians in the 20th Century

In the 20th century, many mathematicians in Russia made great contributions to the field of mathematics. This invaluable book, which presents the main achievements of Russian mathematicians in that century, is the first most comprehensive book on Russian mathematicians.

## Dynamical Systems: A Collection of Papers

This volume consists of very high quality articles which not only give a very good account of this field in the Soviet Union, but also provide stimulating materials for researchers working on this topic.

## Mathematical Problems of Statistical Mechanics (Advanced Nonlinear Dynamics)

## SPDE in Hydrodynamics, Recent Progress and Prospects

## Quantum Fields and Strings: A Course for Mathematicians, Vol. 1

In 1996-97 the Institute for Advanced Study organized a special year-long program designed to teach mathematicians the basic physical ideas which underlie the mathematical applications. These volumes are a written record of the program.

## Quantum Fields and Strings: A Course for Mathematicians, Vol. 2

In 1996-97 the Institute for Advanced Study organized a special year-long program designed to teach mathematicians the basic physical ideas which underlie the mathematical applications. These volumes are a written record of the program.

## Commensurabilities among Lattices in PU (1,n)

The first part of this monograph is devoted to a characterization of hypergeometric-like functions, that is, twists of hypergeometric functions in n-variables.

## Hodge Cycles, Motives and Shimura Varieties (Lecture Notes in Mathematics)

## Modular Functions of One Variable II

## Morse Theory

One of the most cited books in mathematics, John Milnor's exposition of Morse theory has been the most important book on the subject for more than forty years. Morse theory was developed in the 1920s by mathematician Marston Morse. (Morse was on the faculty of the Institute for Advanced Study, and Princeton published his Topological Methods in the Theory of Functions of a Complex Variable in the Annals of Mathematics Studies series in 1947.)

## John Milnor Collected Papers, Volume 1: Geometry

This volume contains papers on geometry of one of the best modern geometers and topologists, John Milnor. This book covers a wide variety of topics and includes several previously unpublished works. It is delightful reading for any mathematician with an interest in geometry and topology and for any person with an interest in mathematics.

## John Milnor Collected Papers, Volume II: The Fundamental Group

The volume contains sixteen papers and is partitioned into four parts: Knot theory, Free action on spheres, Torsion, and Three-dimensional manifolds.

## Collected Papers of John Milnor, Volume III: Differential Topology

## Collected Papers of John Milnor, Volume IV: Homotopy, Homology and Manifolds

The book is divided into four parts: Homotopy Theory, Homology and Cohomology, Manifolds, and Expository Papers. Introductions to each part provide some historical context and subsequent development.

## Collected Papers of John Milnor, Volume V: Algebra

These papers, together with other (some of them previously unpublished) works in algebra are assembled here in this fifth volume of Milnor's Collected Papers. They constitute not only an important historical archive, but also, thanks to the clarity and elegance of Milnor's mathematical exposition, a valuable resource for work in the fields treated.

## Collected Papers of John Milnor, Volume VI: Dynamical Systems

Contains all of Milnor's work on Real and Complex Dynamics from 1953 to 1999, plus one paper from 2000. These papers provide important and fundamental material in real and complex dynamical systems.

## Collected Papers of John Milnor, Volume VII: Dynamical Systems

Together with the preceding Volume VI, it contains all of Milnor's papers in dynamics, through the year 2012. Most of the papers are in holomorphic dynamics; however, there are two in real dynamics and one on cellular automata.

## Lectures on the H-Cobordism Theorem

These are notes for Lectures of John Milnor that were given as a seminar on differential topology in October and November, 1963 Princeton University.

## Prospects in Mathematics

Five papers by distinguished American and European mathematicians describe some current trends in mathematics in the perspective of the recent past and in terms of expectations for the future.

## Topology from the Differentiable Viewpoint

Beginning with basic concepts such as diffeomorphisms and smooth manifolds, Milnor goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, the index number of a map, and the Pontryagin construction are discussed.

## Characteristic Classes

The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds.

## Dynamics in One Complex Variable

This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study.

## Symmetric Bilinear Forms

The theory cf quadratic forms and the intimately related theory of sym- metrie bilinear forms have a lang and rich his tory, highlighted by the work of Legendre, Gauss, Minkowski, and Hasse.

## Singular Points of Complex Hypersurfaces

## Introduction to Algebraic K-Theory

Algebraic K-theory describes a branch of algebra that centers about two functors. K0 and K1, which assign to each associative ring ∧ an abelian group K0∧ or K1∧ respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K2, also from associative rings to abelian groups.

## Class Field Theory

The primary goal of the book was to give a rather complete presentation of algebraic aspects of global class field theory, and the authors accomplished this goal spectacularly: for more than 40 years since its first publication, the book has served as an ultimate source for many generations of mathematicians.

## Collected Works of John Tate: Part 1 (1951-1975)

In these volumes, a reader will find all of John Tate's published mathematical papers-spanning more than six decades-enriched by new comments made by the author. Included also is a selection of his letters. His letters give us a close view of how he works and of his ideas in process of formation.

## Collected Works of John Tate: Part 2 (1976-2006)

In these volumes, a reader will find all of John Tate's published mathematical papers-spanning more than six decades-enriched by new comments made by the author. Included also is a selection of his letters. His letters give us a close view of how he works and of his ideas in process of formation.

## Rational Points on Elliptic Curves

This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry.

## Number Theory, Analysis and Geometry: In Memory of Serge Lang

In the spirit of Lang’s vast contribution to mathematics, this memorial volume contains articles by prominent mathematicians in a variety of areas of the field, namely Number Theory, Analysis, and Geometry, representing Lang’s own breadth of interest and impact. A special introduction by John Tate includes a brief and fascinating account of the Serge Lang’s life.

## Metric Structures for Riemannian and Non-Riemannian Spaces

This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.

## Geometric Topology: Recent Developments

Geometric Topology can be defined to be the investigation of global properties of a further structure (e.g. differentiable, Riemannian, complex,algebraic etc.) one can impose on a topological manifold.

## Moufang Polygons

This book gives the complete classification of Moufang polygons, starting from first principles. In particular, it may serve as an introduction to the various important algebraic concepts which arise in this classification including alternative division rings, quadratic Jordan division algebras of degree three, pseudo-quadratic forms, BN-pairs and norm splittings of quadratic forms.

## Buildings of Spherical Type and Finite BN-Pairs

These notes are a slightly revised and extended version of mim-graphed notes written on the occasion of a seminar on buildings and BN-pairs held at Oberwolfach in April 1968.

## Probability Theory

This volume presents topics in probability theory covered during a first-year graduate course given at the Courant Institute of Mathematical Sciences, USA. The necessary background material in measure theory is developed, including the standard topics, such as extension theorem, construction of measures, integration, product spaces, Radon-Nikodym theorem, and conditional expectation.

## Stochastic Processes

This is a brief introduction to stochastic processes studying certain elementary continuous-time processes. After a description of the Poisson process and related processes with independent increments as well as a brief look at Markov processes with a finite number of jumps, the author proceeds to introduce Brownian motion and to develop stochastic integrals.

## Large Deviations and Applications

Many situations exist in which solutions to problems are represented as function space integrals. Such representations can be used to study the qualitative properties of the solutions and to evaluate them numerically using Monte Carlo methods.

## Lectures on Diffusion Problems and Partial Differential Equations

## Complex Dynamics

A discussion of the properties of conformal mappings in the complex plane, closely related to the study of fractals and chaos. The book ends in a detailed study of the famous Mandelbrot set, which describes very general properties of such mappings.

## Selected Problems on Exceptional Sets

## Linear Algebra and Its Applications

Presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject.

## Functional Analysis

## Complex Proofs of Real Theorems

An extended meditation on Hadamard's famous dictum, "The shortest and best way between two truths of the real domain often passes through the imaginary one."

## Hyperbolic Partial Differential Equations

The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity.

## Scattering Theory, Revised Edition

This revised edition of a classic book, which established scattering theory as an important and fruitful area of research, reflects the wealth of new results discovered in the intervening years.

## Calculus With Applications

Shows that the themes of calculation, approximation, and modeling are central to mathematics and the main ideas of single variable calculus.

## Selected Papers: Volume I

Two volumes span the years from 1952 up until 1999, and cover many varying topics, from functional analysis, partial differential equations, and numerical methods to conservation laws, integrable systems and scattering theory. After each paper, or collection of papers, is a commentary placing the paper in context and where relevant discussing more recent developments.

## Selected Papers: Volume II

Two volumes span the years from 1952 up until 1999, and cover many varying topics, from functional analysis, partial differential equations, and numerical methods to conservation laws, integrable systems and scattering theory. After each paper, or collection of papers, is a commentary placing the paper in context and where relevant discussing more recent developments.

## Partial differential equations: Lectures 1950-1951, With Supplementary Notes

## Michael Atiyah - Collected Works: 7 Volume Set

Atiyah's huge number of published papers, focusing on the areas of algebraic geometry and topology, have here been collected into seven volumes, with the first five volumes divided thematically and the sixth and seventh arranged by date.

## Michael Atiyah: Collected Works: Volume 1: Early Papers; General Papers

## Michael Atiyah: Collected Works: Volume 2: Early Papers on K-Theory

## Michael Atiyah: Collected Works: Volume 3: Index Theory: 1

## Michael Atiyah: Collected Works: Volume 4: Index Theory: 2

## Michael Atiyah: Collected Works: Volume 5: Gauge Theories

## Michael Atiyah Collected Works: Volume 6: 1987-2002

## Michael Atiyah Collected Works: Volume 7: 2002-2013

## Introduction To Commutative Algebra

This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra.

## K-theory

These notes are based on the course of lectures Atiyah gave at Harvard in the fall of 1964. They constitute a self-contained account of vector bundles and K-theory assuming only the rudiments of point-set topology and linear algebra. One of the features of the treatment is that no use is made of ordinary homology or cohomology theory.

## The Geometry and Physics of Knots

Professor Atiyah presents an introduction to Witten's ideas from the mathematical point of view. The book will be essential reading for all geometers and gauge theorists as an exposition of new and interesting ideas in a rapidly developing area.

## A Community of Scholars: Impressions of the Institute for Advanced Study

This beautifully illustrated anthology celebrates eighty years of history and intellectual inquiry at the Institute for Advanced Study, one of the world's leading centers for theoretical research.

## Paul Dirac: The Man and his Work

Together the lectures in this volume, originally presented on the occasion of the dedication ceremony for a plaque honoring Dirac in Westminster Abbey, give a unique insight into the relationship between Dirac's character and his scientific achievements.

## The Geometry and Dynamics of Magnetic Monopoles

In this book a particular system, describing the interaction of magnetic monopoles, is investigated in detail. The use of new geometrical methods produces a reasonably clear picture of the dynamics for slowly moving monopoles.

## Collected Papers of V.K. Patodi

Vijay Kumar Patodi was a brilliant Indian mathematicians who made, during his short life, fundamental contributions to the analytic proof of the index theorem and to the study of differential geometric invariants of manifolds.

## Elliptic Operators and Compact Groups

## Geometry of Yang-Mills Fields

These Lecture Notes are an expanded version of the Fermi Lectures Atiyah gave at Scuola Normale Superiore in Pisa, the Loeb Lectures at Harvard and the Whittemore Lectures at Yale, in 1978.

## Vector Bundles on Algebraic Varieties: Papers presented at the Bombay Colloquium 1984

The purpose of this authoritative volume is to highlight recent developments in the general area of vector bundles as well as principal bundles on both affine and projective varieties.

## Notes on the Lefschetz Fixed Point Theorem for Elliptic Complexes

## Physics and Mathematics of Strings

## Fields Medallist's Lectures

## Vector Fields on Manifolds

This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of exist ence of r linearly independent vector fields.

## Grothendieck-Serre Correspondence (English and French Edition)

This extraordinary volume contains a large part of the mathematical correspondence between A. Grothendieck and J-P. Serre. It forms a vivid introduction to the development of algebraic geometry during the years 1955-1965. During this period, algebraic geometry went through a remarkable transformation

## Oeuvres - Collected Papers I: 1949 - 1959

As listed in the preface, the three volumes cover almost all articles published in mathematical journals between 1949 and 1984, the summaries of the author's courses at the Collège de France since 1956, some of his Séminaire notes, and some items not previously published.

## Oeuvres - Collected Papers II: 1960-1971

As listed in the preface, the three volumes cover almost all articles published in mathematical journals between 1949 and 1984, the summaries of the author's courses at the Collège de France since 1956, some of his Séminaire notes, and some items not previously published.

## Oeuvres - Collected Papers III: 1972 - 1984

Characteristic of Serre's publications are the many open questions he formulated suggesting further research directions. Four volumes specify how he has provided comments on and corrections to most articles, and described the present status of the open questions with reference to later results.

## Oeuvres - Collected Papers IV: 1985 - 1998

This is the fourth volume of J-P. Serre's Collected Papers covering the period 1985-1998. Items, numbered 133-173, contain "the essence" of his work from that period and are devoted to number theory, algebraic geometry, and group theory. Half of them are articles and another half are summaries of his courses in those years and letters. Most courses have never been previously published, nor proofs of the announced results.

## Algebraic Groups and Class Fields

## Local Fields

The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., complete for a discrete valuation) fields with finite residue field.

## Local Algebra

This is an English translation of the now classic "Algbre Locale - Multiplicits" originally published by Springer as LNM 11. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities.

## Trees

The seminal ideas of this book played a key role in the development of group theory since the 70s. Several generations of mathematicians learned geometric ideas in group theory from this book. In it, the author proves the fundamental theorem for the special cases of free groups and tree products before dealing with the proof of the general case.

## Finite Groups: An Introduction

This book is a short introduction to the subject, written both for beginners and for mathematicians at large. There are ten chapters: Preliminaries, Sylow theory, Solvable groups and nilpotent groups, Group extensions, Hall subgroups, Frobenius groups, Transfer, Characters, Finite subgroups of GLn, and Small groups.

## Linear Representations of Finite Groups

This book consists of three parts, rather different in level and purpose. The first part was originally written for quantum chemists. It describes the correspondence, due to Frobenius, between linear representations and characters. The second part is a course given in 1966 to second-year students of l’Ecole Normale. It completes in a certain sense the first part. The third part is an introduction to Brauer Theory.

## Lie Algebras and Lie Groups

The main general theorems on Lie Algebras are covered, roughly the content of Bourbaki's Chapter I. I have added some results on free Lie algebras, which are useful, both for Lie's theory itself (Campbell-Hausdorff formula) and for applications to pro-Jrgroups.

## Abelian l-Adic Representations and Elliptic Curves

This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem.

## Complex Semisimple Lie Algebras

These short notes, already well-known in their original French edition, present the basic theory of semisimple Lie algebras over the complex numbers. The author begins with a summary of the general properties of nilpotent, solvable, and semisimple Lie algebras.

## Cohomological Invariants in Galois Cohomology

This volume addresses algebraic invariants that occur in the confluence of several important areas of mathematics, including number theory, algebra, and arithmetic algebraic geometry. The invariants are analogues for Galois cohomology of the characteristic classes of topology, which have been extremely useful tools in both topology and geometry.

## Topics in Galois Theory: Research Notes in Mathematics

This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group.

## Galois Cohomology

This is an updated English translation of Cohomologie Galoisienne, published more than thirty years ago as one of the very first versions of Lecture Notes in Mathematics. It includes a reproduction of an influential paper by R. Steinberg, together with some new material and an expanded bibliography.

## Lectures on the Mordell-Weil Theorem

The book is based on a course given by J.-P. Serre at the Collège de France in 1980 and 1981. Basic techniques in Diophantine geometry are covered, such as heights, the Mordell-Weil theorem, Siegel's and Baker's theorems, Hilbert's irreducibility theorem, and the large sieve.

## Prospects in Mathematics

Five papers by distinguished American and European mathematicians describe some current trends in mathematics in the perspective of the recent past and in terms of expectations for the future.