本书是复分析入门的首选，既可以用作教材，也可以用来自学。高年级本科生、低年级研究生、熟悉高等微积分或具备实分析入门知识的读者均可阅读本书。除幂级数、柯西定理、留数、共形映射和调和函数等标准材料外，本书还对同类书中不常见的有趣的主题做了清晰论述。附加的主题和应用使本书既适用于一学期课程，也适用于全年课程。
详细的习题解答既可给学生做示范，也可促进自学。书中未包含解答的补充练习则提供了一种额外的教学工具。

Preface to the Second Edition
Preface to the First Edition
To the Student
Chapter 1 From Complex Numbers to Cauchy's Theorem
1.Complex Numbers
2.Functions
3.Power Series
4.Some Elementary Functions
5.Curves and Integrals
6.Cauchy's Theorem
Chapter 2 Applications of Cauchy's Theorem
7.Cauchy's Integral Formula
8.Isolated Singular Points
9.Evaluation of Definite Integrals
10.Logarithms and General Powers
11.Additional Definite Integrals
12.Zeros of Analytic Functions
13.Univalence and Inverses
14.Laurent Series
15.Combinations of Power Series and Laurent Series
16.The Maximum Principle
Chapter 3 Analytic Continuation
17.The Idea of Analytic Continuation
18.Power Series on the Circle of Convergence
Chapter 4 Harmonic Functions and Conformal Mapping
19.Harmonic Functions
20.Harmonic Functions in a Disk
*21.Harmonic Functions and Fourier Series
22.Conformal Mapping
23.Some Applications of Conformal Mapping to Physics
24.Some Special Flows
25.Mobius Transformations
26.Further Examples of Transformations and Flows
27.Dirichlet Problems in General
28.The Riemann Mapping Theorem
29.Intuitive Riemann Surfaces
Chapter 5 Miscellaneous Topics
30.A Non-Euclidean Geometry
31.Infinite Products
32.Rate of Growth Versus Number of Zeros
33.Generalizations of the Maximum Principle
34.Asymptotic Series
35.Univalent Functions in the Disk
Solutions of Exercises
References
Index
About the Authors