重要的数学书
1. Serge Lang系列：
Linear Algebra - 2nd
Undergraduate Algebra
Algebra - 3rd
Short Calculus
Calculus of Several Variables
Undergraduate Analysis - 2nd
Complex Analysis - 4th
Real and Functional Analysis - 3rd
Fundamentals of Differential Geometry
Introduction to Algebraic Geometry
2. Walter Rudin系列：
Principles of Mathematical Analysis - 3rd
Real and Complex Analysis - 3rd
Functional Analysis - 2nd
3. Elias M. Stein系列：
Fourier Analysis: An Introduction
Complex Analysis
Real Analysis: Measure Theory, Integration, and Hilbert Spaces
Functional Analysis: Introduction to Further Topics in Analysis
Introduction to Fourier Analysis on Euclidean Spaces
Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals
4. Hermann Weyl系列：
The Classical Groups: Their Invariants and Representations
Die Idee der Riemannschen Fläche
The Concept of a Riemann Surface
Einführung in die Funktionentheorie
The Theory of Groups and Quantum Mechanics
Philosophy of Mathematics and Natural Science
Symmetry
Raum · Zeit · Materie: Vorlesungen über Allgemeine Relativitätstheorie
5. G. H. Hardy系列：
An Introduction to the Theory of Numbers - 6th
A Course of Pure Mathematics - 10th
6. Richard Courant系列：
What Is Mathematics
Introduction to Calculus and Analysis
Differential and Integral Calculus
Methods of Mathematical Physics
7. 代数：
代数学引论（1，2，3卷）
Algebra I - Neunte Auflage - B.L. van der Waerden
Algebra II - Sechste Auflage - B.L. van der Waerden
Algebra - 2nd - Michael Artin
Applied Analysis - John K. Hunter
Galois Theory - 2nd - Emil Artin
Galois Theory - Harold M. Edwards
Introduction to Lie Algebras and Representation Theory - James Humphreys
Abstract Algebra - 3rd- I. N. Herstein
Linear Algebra - 2nd - Kenneth Hoffman
Linear Algebra done right - 2nd - Sheldon Axler
Commutative Algebra - Oscar Zariski
Advanced Linear Albebra - Steven Roman
Linear Algebra and Its Applications - 4th - Gilbert Strang
8. 分析：
Calculus - 3rd - Michael Spivak
Analysis 1 - Sechste Auflage - Wolfgang Walter
Analysis 2 - Sechste Auflage - Wolfgang Walter
A Course of Modern Analysis - 4th - E.T.Whittaker
Calculus on Manifolds - Michael Spivak
Analysis on Manifolds - James R. Munkres
Theory and Application of Infinite Series - Konrad Knopp
Theorie und Anwendung der unendlichen Reihen - Dritte Auflage - Konrad Knopp
Theory of Complex Functions - Reinhold Remmert
Classical Topics in Complex Function Theory - Reinhold Remmert
Funktionentheorie - Reinhold Remmert
Introductory Functional Analysis with Applications - Erwin Kreyszig
Elements of the Theory of Functions and Functional Analysis - A. N. Kolmogorov
A Student's Guide to Fourier Transforms - 3rd - J. F. James
Fourier Analysis - T. W. Körner
Fourier Series and Integrals - H. Dym
A panorama of Harmonic Analysis - Steven G. Krantz
Trigonometric Series - 3rd - A. Zygmund
The Fast Foruier Transform and Its Applications - E. Oran Brigham
An Introduction to Harmonic Analysis - 3rd - Yitzhak Katznelson
The Fourier Transform and Its Applications - 3rd - Ronald N. Bracewell
Partial Differential Equations - 2nd - Lawrence C. Evans
Calculus of Variations: with Applications to Physics and Engineering - Robert Weinstock
Calculus of Variations - I. M. Gelfand
Ordinary Differential Equations V.I. Arnold
Differential Equations and Their Applications - 4th - Martin Braun
Differential Equations, Dynamical Systems, and Linear Algebra - Morris W. Hirsch
A First Course in Differential Equations with Modeling Applications - 7th - Dennis G. Zill
Numerical Methods for Scientists and Engineers - R. W. Hamming
Vector Calculus, Linear Algebra, and Differential Forms - John Hamal Hubbard
9. 几何、拓扑、微分几何
Basic Topology - M. A. Armstrong
Topology - James Munkres
Lehrbuch Der Topologie - H. Seifert
Algebraic Topology: An Introduction - William S. Massey
Singular Homology Theory - William S. Massey
Differential Topology - Morris W. Hirsch
Topology: from the Differentiable Viewpoint - John Willard Milnor
Differential Geometry: Curves - Surfaces - Manifolds - 2nd - Wolfgang Kühnel
Differentialgeometrie: Kurven - Flächen - Mannigfaltigkeiten - 4.Auflage - Wolfgang Kühnel
微分几何讲义 - 第二版 - 陈省身
Differential Geometry of Curves and Surfaces - Manfredo P. do Carmo
Riemannian Geometry - Manfredo P. do Carmo
10. 概率
Foundations of The Theory of Probability - A. N. Kolmogorov
Introduction to Probability Theory - Paul G. Hoel
An Introduction to Probability Theory and Its Applications -2nd - William Feller
Probability Theory: A Concise Course - Y.A. Rozanov
Introduction to Probability - Joseph K. Blitzstein
11. 数学哲学、数学史等：
A Hstory of Mathematics - 3rd Uta C. Merzbach
高观点下的初等数学 - Felix Klein
数学在19世纪的发展 - Felix Klein
Linear Algebra - 2nd
Undergraduate Algebra
Algebra - 3rd
Short Calculus
Calculus of Several Variables
Undergraduate Analysis - 2nd
Complex Analysis - 4th
Real and Functional Analysis - 3rd
Fundamentals of Differential Geometry
Introduction to Algebraic Geometry
2. Walter Rudin系列：
Principles of Mathematical Analysis - 3rd
Real and Complex Analysis - 3rd
Functional Analysis - 2nd
3. Elias M. Stein系列：
Fourier Analysis: An Introduction
Complex Analysis
Real Analysis: Measure Theory, Integration, and Hilbert Spaces
Functional Analysis: Introduction to Further Topics in Analysis
Introduction to Fourier Analysis on Euclidean Spaces
Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals
4. Hermann Weyl系列：
The Classical Groups: Their Invariants and Representations
Die Idee der Riemannschen Fläche
The Concept of a Riemann Surface
Einführung in die Funktionentheorie
The Theory of Groups and Quantum Mechanics
Philosophy of Mathematics and Natural Science
Symmetry
Raum · Zeit · Materie: Vorlesungen über Allgemeine Relativitätstheorie
5. G. H. Hardy系列：
An Introduction to the Theory of Numbers - 6th
A Course of Pure Mathematics - 10th
6. Richard Courant系列：
What Is Mathematics
Introduction to Calculus and Analysis
Differential and Integral Calculus
Methods of Mathematical Physics
7. 代数：
代数学引论（1，2，3卷）
Algebra I - Neunte Auflage - B.L. van der Waerden
Algebra II - Sechste Auflage - B.L. van der Waerden
Algebra - 2nd - Michael Artin
Applied Analysis - John K. Hunter
Galois Theory - 2nd - Emil Artin
Galois Theory - Harold M. Edwards
Introduction to Lie Algebras and Representation Theory - James Humphreys
Abstract Algebra - 3rd- I. N. Herstein
Linear Algebra - 2nd - Kenneth Hoffman
Linear Algebra done right - 2nd - Sheldon Axler
Commutative Algebra - Oscar Zariski
Advanced Linear Albebra - Steven Roman
Linear Algebra and Its Applications - 4th - Gilbert Strang
8. 分析：
Calculus - 3rd - Michael Spivak
Analysis 1 - Sechste Auflage - Wolfgang Walter
Analysis 2 - Sechste Auflage - Wolfgang Walter
A Course of Modern Analysis - 4th - E.T.Whittaker
Calculus on Manifolds - Michael Spivak
Analysis on Manifolds - James R. Munkres
Theory and Application of Infinite Series - Konrad Knopp
Theorie und Anwendung der unendlichen Reihen - Dritte Auflage - Konrad Knopp
Theory of Complex Functions - Reinhold Remmert
Classical Topics in Complex Function Theory - Reinhold Remmert
Funktionentheorie - Reinhold Remmert
Introductory Functional Analysis with Applications - Erwin Kreyszig
Elements of the Theory of Functions and Functional Analysis - A. N. Kolmogorov
A Student's Guide to Fourier Transforms - 3rd - J. F. James
Fourier Analysis - T. W. Körner
Fourier Series and Integrals - H. Dym
A panorama of Harmonic Analysis - Steven G. Krantz
Trigonometric Series - 3rd - A. Zygmund
The Fast Foruier Transform and Its Applications - E. Oran Brigham
An Introduction to Harmonic Analysis - 3rd - Yitzhak Katznelson
The Fourier Transform and Its Applications - 3rd - Ronald N. Bracewell
Partial Differential Equations - 2nd - Lawrence C. Evans
Calculus of Variations: with Applications to Physics and Engineering - Robert Weinstock
Calculus of Variations - I. M. Gelfand
Ordinary Differential Equations V.I. Arnold
Differential Equations and Their Applications - 4th - Martin Braun
Differential Equations, Dynamical Systems, and Linear Algebra - Morris W. Hirsch
A First Course in Differential Equations with Modeling Applications - 7th - Dennis G. Zill
Numerical Methods for Scientists and Engineers - R. W. Hamming
Vector Calculus, Linear Algebra, and Differential Forms - John Hamal Hubbard
9. 几何、拓扑、微分几何
Basic Topology - M. A. Armstrong
Topology - James Munkres
Lehrbuch Der Topologie - H. Seifert
Algebraic Topology: An Introduction - William S. Massey
Singular Homology Theory - William S. Massey
Differential Topology - Morris W. Hirsch
Topology: from the Differentiable Viewpoint - John Willard Milnor
Differential Geometry: Curves - Surfaces - Manifolds - 2nd - Wolfgang Kühnel
Differentialgeometrie: Kurven - Flächen - Mannigfaltigkeiten - 4.Auflage - Wolfgang Kühnel
微分几何讲义 - 第二版 - 陈省身
Differential Geometry of Curves and Surfaces - Manfredo P. do Carmo
Riemannian Geometry - Manfredo P. do Carmo
10. 概率
Foundations of The Theory of Probability - A. N. Kolmogorov
Introduction to Probability Theory - Paul G. Hoel
An Introduction to Probability Theory and Its Applications -2nd - William Feller
Probability Theory: A Concise Course - Y.A. Rozanov
Introduction to Probability - Joseph K. Blitzstein
11. 数学哲学、数学史等：
A Hstory of Mathematics - 3rd Uta C. Merzbach
高观点下的初等数学 - Felix Klein
数学在19世纪的发展 - Felix Klein