本书是作者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。本书内容包括实数、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。

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 ODE's

 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 Cavalieri's 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 Lebesgue's Fundamental Theorem of Calculus

 9 Lebesgue's Last Theorem

 Appendix A: Translations and Nonmeasurable sets

 Appendix B: The Banach-Tarski Paradox

 Appendix C: Riemann integrals as undergraphs

 Appendix D: Littlewood's Three Principles

 Appendix E: Roundness

 Appendix F: Money

 Suggested Reading

 Bibliography

 Exercises

Index