作者Pugh在伯克利大学讲授数学分析课程30多年之久的基础上编写而成，书中语言表述生动活泼、通俗易懂，引用了很多有价值的例子以及来自Dieudonne，Littlewood和Osserman等几位数学家的评论，还精心挑选了500多个精彩的练习题。《实数学分析（影印版）》内容包括实数、拓扑知识初步、实变函数、函数空间、多元微积分、Lebesgue积分理论等，其中多元微积分的讲法较为接近当前数学界常用的语言，将会对我国数学分析的教学产生积极的影响。

　　为了更好的借鉴国外数学教育与研究的成功经验，促进我国的数学教育与研究事业的发展，提高高等学校数学教育教学质量，本着“为我国热爱数学的 青年创造一个较好的学习环境”这一宗旨，天元基金赞助出版“天元基金影印数学丛书”。
　　该丛书主要包含国外反映近代数学发展的纯数学与应用数学方面的优秀书籍，天元基金邀请国内各个方向的知名数学家参与选题的工作，经专家遴选，推荐，由高等教育出版社影印出版。为了提高我国数学研究生教学的水平，暂把选书的 目标确定在研究生教材上。当然，有的书也可以作为本科生教材或参考书，有的书则介于研究生教材与专著之间。
　　欢迎各方专家，读者对本丛书的选题，印刷，销售等工作提出批评和建议。

1 Real Numbers
1 Preliminaries
2 Cuts
3 Euclidean Space
4 Cardinality
5* Comparing Cardinalities
6* The Skeleton of Calculus
Exercises
2 A Taste of Topology
1 Metric Space Concepts
2 Compactness
3 Connectedness
4 Coverings
5 Cantor Sets
6* Cantor Set Lore
7* Completion
Exercises
3 Functions of a Real Variable
1 Differentiation
2 Riemann Integration
3 Series
Exercises
4 Function Spaces
1 Uniform Convergence and C0[a, b]
2 Power Series
3 Compactness and Equicontinuity in CO
4 Uniform Approximation in Co
5 Contractions and ODEs
6* Analytic Functions
7* Nowhere Differentiable Continuous Functions
8* Spaces of Unbounded Functions
Exercises
5 Multivariable Calculus
1 Linear Algebra
2 Derivatives
3 Higher derivatives
4 Smoothness Classes
5 Implicit and Inverse Functions
6* The Rank Theorem
7* Lagrange Multipliers
8 Multiple Integrals
9 Differential Forms
10 The General Stokes Formula
11* The Brouwer Fixed Point Theorem
Appendix A: Perorations of Dieudonne
Appendix B: The History of Cavalieris Principle
Appendix C: A Short Excursion into
the Complex Field
Appendix D: Polar Form
Appendix E: Determinants
Exercises
6 Lebesgue Theory
1 Outer measure
2 Measurability
3 Regularity
4 Lebesgue integrals
5 Lebesgue integrals as limits
6 Italian Measure Theory
7 Vitali coverings and density points
8 Lebesgues Fundamental Theorem of Calculus
9 Lebesgues Last Theorem
Appendix A: Translations and Nonmeasurable sets
Appendix B: The Banach-Tarski Paradox
Appendix C: Riemann integrals as undergraphs
Appendix D: Littlewoods Three Principles
Appendix E: Roundness
Appendix F: Money
Suggested Reading
Bibliography
Exercises
Index