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Bibliography for Mathematics

Algebra

    1. Weber

    • Lehrbuch der Algebra

      • Vol 1

      • Vol 2

      • Vol 3

      1. van der Waerden

    • Algebra

      • I

      • II

    • A History of Algebra: From al-Khwārizmī to Emmy Noether

    1. Artin

    • Galois Theory: Lectures Delivered at the University of Notre Dame

    • Geometric Algebra

    • Exposition by Emil Artin (A Selection)

    1. Artin

    • Algebra

    1. Lang

    • Algebra

    1. Jacobson

    • Basic Algebra, Vol. 1

    • Basic Algebra, Vol. 2

    • Lectures in Abstract Algebra

      • I: Basic Concepts

      • II: Linear Algebra

      • III: Theory of Fields and Galois Theory

      1. Cohn

    • Basic Algebra: Groups, Rings and Fields

    • Further Algebra and Applications

    1. MacLane

    • Categories for the Working Mathematician

    • Homology

  • J.-P. Serre

    • Lie Algebras and Lie Groups

    • Linear Representations of Finite Groups

    • Topics in Galois Theory

    • Finite Groups: An Introduction

      1. Shafarevich

    • Discourses on Algebra

      1. Shafarevich, A. I. Kostrikin

    • Basic Notions of Algebra

      1. Gelfand, Yu. I. Manin

    • Methods of Homological Algebra

    1. Chevalley

    • Fundamental Concepts of Algebra

    • The Theory of Lie Groups

    • Introduction to the theory of Algebraic Functions of One Variable

Commutative Algebra

    1. Atiyah, I. G. MacDonald

    • Introduction to Commutative Algebra

    1. Eisenbud

    • Commutative Algebra, with a view towards Algebraic Geometry

Analysis

Real Analysis

    1. Royden

    • Real Analysis

      1. Apostol

    • Mathematical Analysis

    1. Rudin

    • Principles of Mathematical Analysis

    • Real and Complex Analysis

    1. Tao

    • Analysis

      • I

      • II

      1. Lieb, M. Loss

    • Analysis

      1. Stein, R. Shakarchi

    • Real Analysis: Meausure Theory, Integration and Hilbert Spaces

    1. Hurewicz

    • Lectures on Ordinary Differential Equations

    1. Ya. Khinchin

    • A Course of Mathematical Analysis

      1. Hardy

    • A Course in Pure Mathematics

    1. Rudin

    • Fourier Analysis on Groups

    1. Nachbin

    • The Haar Integral

      1. Stein, R. Shakarchi

    • Fourier Analysis: An Introduction

Functional Analysis

      1. Simmons

    • Introduction to Topology and Modern Analysis

      1. Stein, R. Shakarchi

    • Functional Analysis: Introduction to Further Topics in Analysis

    1. Rudin

    • Functional Analysis

    1. Yosida

    • A Course in Functional Analysis

      1. Conway

    • Functional Analysis

    1. Einsiedler, T. Ward

    • Functional Analysis, Spectral Theory, and Applications

Complex Analysis

      1. Ahlfors

    • Complex Analysis

      1. Conway

    • Functions of One Complex Variable

    1. Narasimhan, Y. Nievergelt

    • Complex Analysis in One Variable

    1. Narasimhan

    • Several Complex Variables

    • Analysis on Real and Complex Manifolds

      1. Stein, R. Shakarchi

    • Complex Analysis

Probability and Statistics

      1. Kolmogorov

    • Foundations of the Theory of Probability

      1. Shiryayev

    • Probability

    1. Feller

    • An Introduction to Probability Theory and its Applications

      • Vol. 1

      • Vol. 2

      1. Hoel, S. C. Port, C. J. Stone

    • Introduction to Probability Theory

    • Introduction to Statistical Theory

    • Introduction to Stochastic Processes

      1. Bain, M. Engelhardt

    • Introduction to Probability and Mathematical Statistics

    1. Karlin, H. M. Taylor

    • A first course in Stochastic Processes

    • A second course in Stochastic Processes

    • An introduction to Stochastic Modelling

      1. Rosenthal

    • A first look at Rigorous Probability Theor

        1. Seber

    • Multivariate Observations

    1. Grimmett, D. Stirzaker

    • Probability and Random Processes

    1. Williams

    • Probability with Martingales

Dynamical Systems and Ergodic Theory

    1. Walters

    • An Introduction to Ergodic Theory

    1. Ward, M. Einsiedler

    • Ergodic Theory: with a view towards Number Theory

    1. Barreira, Y. Pesin

    • Introduction to Smooth Ergodic Theory

    1. Barreira

    • Ergodic Theory, Hyperbolic Dynamics and Dimension Theory

      1. Bowen

    • Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms

    1. Katok, B. Hasselblatt

    • Introduction to the Modern Theory of Dynamical Systems

    1. Katok (ed.)

    • Ergodic Theory and Dynamical Systems I: Proceedings Special Year, Maryland 1979-80

    • Ergodic Theory and Dynamical Systems II: Proceedings Special Year, Maryland 1979–80

    1. Katok, Y. Pesin, F. R. Hertz (eds)

    • Modern Theory of Dynamical Systems: A Tribute to Dmitry Victorovich Anosov

    1. Bedford, M. Keane, C. Series (eds)

    • Ergodic Theory, Symbolic Dynamics, and Hyperbolic Spaces

    1. Milnor

    • Dynamics in One Complex Variable: Introductory Lectures

    1. Koladya, Yu. Manin, M. Moeller, P. Moree, T. Ward (eds)

    • Dynamical Numbers: Interplay Between Dynamical Systems and Number Theory

Geometry

        1. Coxeter

    • Introduction to Geometry

    • Projective Geometry

    • Real Projective Plane

    • The Beauty of Geometry: Twelve Essays

    • Non-Euclidean Geometry

    • Geometry Revisited

Topology

      1. Munkres

    • Topology

      1. Kelly

    • Topology

      1. Armstrong

    • Basic Topology

      1. Bredon

    • Topology and Geometry

      1. Singer, J. A. Thorpe

    • Lecture Notes on Elementary Topology and Geometry

Algebraic Topology

    1. Artin, H. Braun

    • Introduction to Algebraic Topology

    1. Dold

    • Lectures on Algebraic Topology

    1. Hatcher

    • Algebraic Topology

      1. Greenberg, J. R. Harper

    • Algebraic Topology: A First Course

      1. Munkres

    • Elements of Algebraic Topology

      1. Spanier

    • Algebraic Topology

      1. Massey

    • Algebraic Topolgy: An Introduction

    1. Fulton

    • Algebraic Topology: A First Course

      1. May

    • A Concise Course in Algebraic Topology

    • Simplicial Objects in Algebraic Topology

    1. Eilenberg, N. Steenrod

    • Foundations of Algebraic Topology

      1. Matveev

    • Lectures on Algebraic Topology

Differential Topology

      1. Warner

    • Foundations of Differentiable Manifolds and Lie Groups

      1. Milnor

    • Topology from the Differentiable Viewpoint

    • Morse Theory

    1. Milnor, J. D. Stasheff

    • Charecteristic Classes

    1. Ramanan

    • Global Calculus

    1. Kreck

    • Differential Algebraic Topology: From Stratifolds to Exotic Spheres

    1. Bott, L. W. Tu

    • Differential Forms in Algebraic Topology

Teichmüller Spaces

    1. Imayoshi, M. Taniguchi

    • An Introduction to Teichmüller Spaces

    1. Farb, D. Margalit

    • A Primer on Mapping Class Groups

      1. Silva Satos

    • Dynamical Aspects of Teichmüller Theory: SL(2,R)-Action on Moduli Spaces of Flat Surfaces

Differential Geometry

      1. Thorpe

    • Elementary Topics in Differential Geometry

    1. Helgason

    • Differential Geometry, Lie Groups, and Symmetric Spaces

    1. Kobayashi, K. Nomizu

    • Foundations of Differential Geometry

      • Vol 1

      • Vol 2

Algebraic Geometry

      1. Smith, L. Kahanpaa, P. Kekkalainen, W. Traves

    • An Invitation to Algebraic Geometry

    1. Miranda

    • Algebraic Curves and Riemann Surfaces

    1. Hartshorne

    • Algebraic Geometry

    • Residues and Duality

      1. Shafarevich

    • Basic Algebraic Geometry

      • 1: Varieties in Projective Space

      • 2: Schemes and Complex Manifolds

    1. Harris

    • Algebraic Geometry: A First Course

    1. Mumford

    • The Red Book of Varieties and Schemes

    • Curves and their Jacobians

    • Algebraic Geometry I: Complex Projective Varieties

    • Lectures on Curves on an Algebraic Surface

    • Abelian Varieties

    • Tata Lectures on Theta

      • I

      • II: Jacobian Theta Functions and Differential Equations

      • III

    1. Mumford, T. Oda

    • Algebraic Geometry - II

      sequel to the Red Book.

    1. Mumford, J. Fogarty, F. Kirwan

    • Geometric Invariant Theory

    1. Eisenbud, J. Harris

    • The Geometry of Schemes

    1. Griffiths, J. Harris

    • Principles of Algebraic Geometry

    1. Arbarello, M. Cornalba, P. Griffiths, J. Harris

    • Geometry of Algebraic Curves

      • Vol I

      • Vol II

  • Yu. I. Manin

    • Introduction to the Theory of Schemes (Moscow Lectures)

    1. Hirzebruch

    • Topological Methods in Algebraic Geometry

    1. Harder

    • Lectures on Algebraic Geometry

      • I, Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces

      • II Basic Concepts, Coherent Cohomology, Curves and their Jacobians

    1. Cartier, G. Laumon, L. Illusie, Yu. I. Manin, N. M. Katz, K. A. Ribet

    • Grothendieck Festshrift

      • Vol 1

      • Vol 2

      • Vol 3

    1. Voisin

    • Hodge Theory and Complex Algebraic Geometry

      • I

      • II

      1. Dolgachev

    • Classical Algebraic Geometry: A Modern View

    1. Harris, I. Morrison

    • Moduli of Curves

    1. Fulton

    • Algebraic Curves: An Introduction to Algebraic Geometry

    • Introduction to Intersection Theory in Algebraic Geometry

    1. Fantechi, L. Gottsche, L. Illusie, S. L. Kleiman, N. Nitsure, A. Vistoli

    • Fundamental Algebraic Geometry: Grothendieck's FGA Explained

    1. Ueno

    • Algebraic Geometry

      • 1 From Varieties to Schemes

      • 2 Sheaves and Cohomology

      • 3 Further Study of Schemes

    1. Weil

    • Foundations of Algebraic Geometry

    1. Huybrechts

    • Fourier-Mukai Transforms in Algebraic Geometry

      1. Clemens

    • A Scrapbook of Complex Curve Theory

    1. Brieskorn, H. Knörrer

    • Plane Algebraic Curves

Theory of Numbers

Elementary Number Theory

    1. Ya. Khinchin

    • Three Pearls of Number Theory

    • Continued Fractions

      1. Hardy, E. M. Wright

    • An Introduction to the Theory of Numbers

    1. Davenport

    • The Higher Arithmetic: An Introduction to the Theory of Numbers

    1. Weil

    • Number Theory: An Approach Through History from Hammurapi to Legendre

    • Number Theory for Beginners

    1. Rademacher

    • Lectures on Elementary Number Theory

    1. Ireland, M. Rosen

    • A Classical Introduction to Modern Number Theory

    1. Koblitz

    • A Course in Number Theory and Cryptography

    1. Niven, H. S. Zuckerman, H. L. Montgomery

    • An Introduction to the Theory of Numbers

Analytic Number Theory

      1. Apostol

    • Introduction to Analytic Number Theory

    • Modular Functions and Dirichlet Series in Number Theory

    1. Chandrasekharan

    • Introduction to Analytic Number Theory

  • J-P. Serre

    • A course in Arithmetic

    1. Artin

    • The Gamma Function

    1. Rademacher

    • Topics in Analytic Number Theory

    • Dedekind Sums

    1. Ivic

    • The Riemann Zeta Function: Theory and Applications

      1. Titchmarsh, R. Heath-Brown

    • The Theory of the Riemann Zeta Function

    1. Iwaniec

    • Lectures on the Riemann Zeta Function

    1. Iwaniec, E Kowalski

    • Analytic Number Theory

      1. Montgomery

    • Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis

    • Topics in Multiplicative Number Theory

      1. Montgomery, R. C. Vaughn

    • Multiplicative Number Theory - I

      1. Edwards

    • Riemann's Zeta Function

      1. Karatsuba

    • Basic Analytic Number Theory

      1. Davenport

    • Multiplicative Number Theory

Algebraic Number Theory

    1. Narasimhan

    1. Neukirch

    • Algebraic Number Theory

    • Class Field Theory: The Bonn Lectures

    1. Hecke

    • Lectures on the Theory of Algebraic Numbers

    1. Weil

    • Basic Number Theory

    • Elliptic Functions According to Eisenstein and Kronecker

    • Adeles and Algebraic Groups

      1. Cassels, A. Frohlich (eds)

    • Algebraic Number Theory

    1. Koch

    • Number Theory: Algebraic Numbers and Functions

    • Algebraic Number Theory

    1. Artin

    • Algebraic Numbers and Algebraic Functions

    1. Artin, J. T. Tate

    • Class Field Theory

      1. Washington

    • Introduction to Cyclotomic Fields

    1. Lang

    • Algebraic Number Theory

    • Cyclotomic Fields I and II

  • Yu. I. Manin, A. A. Panchishkin

    • Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories

  • J.-P. Serre

    • Local Fields

    • Galois Cohomology

    1. Koblitz

    • P-adic numbers, p-adic analysis, and zeta-functions

Arithmetic Algebraic Geometry

    1. Liu

    • Algebraic Geometry and Arithmetic Schemes

    1. Conrad, K. Rubin

    • Arithmetic Algebraic Geometry (IAS/Park City Mathematics)

  • J.-P. Serre

    • Algebraic Groups and Class Fields

    • Lectures on N_x(p)

    1. Cornell, J. H. Silverman

    • Arithmetic Geometry

    1. Bosch, W. Lütkebohmert, M. Raynaud

    • Néron Models

      1. Tate, B. Mazur, J.-P. Serre

    • Collected Works of John Tate

      • 1951-1975 Part 1

      • 1976-2006 Part 2

Elliptic Curves

        1. Cassels

    • Lectures on Elliptic Curves

  • J.-P. Serre

    • Lectures on the Mordell-Weil Theorem

    • Abelian l-adic Representations and Elliptic Curves

      1. Silverman, J. T. Tate

    • Rational Points on Elliptic Curves

      1. Silverman

    • The Arithmetic of Elliptic Curves

    • Advanced Topics in the Arithmetic of Elliptic Curves

      1. Washington

    • Elliptic Curves: Number Theory and Cryptography

      1. Knapp

    • Elliptic Curves

    1. Husemoller

    • Elliptic Curves

    1. Koblitz

    • Introduction to Elliptic Curves and Modular Forms

      1. Katz, B. Mazur

    • Arithmetic Moduli of Elliptic Curves

    1. Hida

    • Geometric Modular Forms and Elliptic Curves

    1. Cornell, J. H. Silverman

    • Modular Forms and Fermat's Last Theorem

Automorphic Forms

    1. Miyake

    • Modular Forms

    1. Shimura

    • Introduction to the Arithmetic Theory of Automorphic Functions

    • Elementary Dirichlet Series and Modular Forms

    • Euler Products and Eisenstein Series

    • Abelian Varieties with Complex Multiplication and Modular Functions

    • Arithmeticity in the Theory of Automorphic Forms

    • Modular Forms: Basics and Beyond

    • Arithmetic of Quadratic Forms

    • Automorphic Functions and Number Theory

    • Arithmetic and Analytic Theories of Quadratic Forms and Clifford Groups

    • Collected Papers

      • Vol 1

      • Vol 2

      • Vol 3

      • Vol 4

    1. Weil

    • Dirichlet Series and Automorphic Forms

    1. Diamond, J. Shurman

    • A First Course in Modular Forms

    1. Lehner

    • Lectures on Modular Forms

      1. Gunning

    • Lectures on Modular Forms

Reflections and Autobiographies

    1. Shimura

    • The Map of My Life

    1. Weil

    • Apprencticeship of a Mathematician

      1. Rota

    • Indiscrete Thoughts

  • Yu. I. Manin

    • Mathematics as Metaphor

      1. Krantz

    • Mathematical Apocrypha

    • Mathematical Apocrypha Redux: More Stories and Anecdotes of Mathematicians and the Mathematical

    1. Grothendieck, J.-P. Serre

    • Grothendieck - Serre Correspondence