首先，这部书讲清楚了泛函分析理论对数学其他领域的应用。其次，这部书讲清楚了分析理论在诸多领域(如物理学、化学、生物学、工程技术和经济学等等)的广泛应用。再次，该书由浅入深地讲透了基本理论的发展历程及走向，它既讲清楚了所涉及学科的具体问题，也讲清楚了其背后的数学原理及其作用。

这套书的写作起点很低，具备本科数学水平就可以读；应用都是从最简单情形入手，应用领域的读者也可以读；全书材料自足，各部分又尽可能保持独立；书后附有极其丰富的参考文献及一些文献评述；该书文字优美，引用了许多大师的格言，读之你会深受启发。

Preface to the Second Corrected Printing

Preface to the First Printing

Introduction

FUNDAMENTAL FIXED-POINT PI~INCIPLES

 CHAPTER 1 The Banach Fixed-Point Theorem and Iterative Methods

1.1. The Banach Fixed-Point Theorem

 1.2. Continuous Dependence on a Parameter

 1.3. The Significance of the Banach Fixed-Point Theorem

 1.4. Applications to Nonlinear Equations

 1.5. Accelerated Convergence and Newton's Method

 1.6. The Picard-Lindel6f Theorem

 1.7. The Main Theorem for Iterative Methods for Linear Operator Equations

 1.8. Applications to Systems of Linear Equations

 1.9. Applications to Linear Integral Equations

 CHAPTER 2 The Schauder Fixed-Point Theorem and Compactness

APPLICATIONS OF THE FUNDAMENTAL FIXED-POINT PRINCIPLES

 CHAPTER 3 Ordinary Differential Equations in B-spaces

 CHAPTER 4 Differential Calculus and the Implicit Function Theorem

 CHAPTER 5 Newton's Method

 CHAPTER 6 Continuation with Respect to a Parameter

 CHAPTER 7 Positive Operators

 CHAPTER 8 Analytic Bifurcation Theory

 CHAPTER 9 Fixed Points of Multivalued Maps

 CHAPTER 10 Nonexpansive Operators and Itertive Methods

 CHAPTER 11 Condensing Maps and the Bourbaki-Kneser Fixed-Point Theorem

THE MAPPING DEGREE AND THE FIXED-POINT INDEX

Appendix

References

Additional References to the Second Printing

List of Symbols

List of Theorems

List of the Most Important Definitions

Schematic Overviews

General References to the Literature

List of Important Principles

Contents of the Other Parts

Index