本教材是学习泛函分析课程的一本入门教材，是针对中国学生编写的一本英文教材，在选材上吸收了国外的很好本科生教材的一些精华；在编写上考虑了与中国学生所具备的基础知识衔接性，在充分地反映泛函分析中的核心内容的前提下，突出重点；在内容的处理上，体现了由浅入深，循序渐进的原则，用大量的例题对度量空间、赋范线性空间、线性算子与线性泛函、内积空间与各种算子及它们的谱分解的概念、关系、性质进行了演绎、推导与论证，书后的索引有中英文对照翻译，便于读者自学。本书配有200多道练习题（部分习题附有提示），为读者掌握泛函分析方法提供必要的训练。

Preface
Introduction
List of Symbols
Chapter 1 Metric Spaces
1.1 Preliminaries
1.2 Definitions and Examples
1.3 Convergence of Sequences in Metric Spaces
1.4 Sets in a Metric Space
1.5 Complete Metric Spaces
1.6 Continuous Mappings on Metric Spaces
1.7 Compact Metric Spaces
1.8 Banach Fixed Point Theorem
Chapter 2 Normed Linear Spaces.Banach Spaces
2.1 Review of Linear Spaces
2.2 Norms in Linear Spaces
2.3 Examples of Normed Linear Spaces
2.4 Finite-Dimensional Normed Linear Spaces
2.5 Linear Subspaces of Normed Linear Spaces
2.6 Quotient Spaces
2.7 Weierstrass Approximation Theorem
Chapter 3 Inner Product Spaces.Hilbert Spaces
3.1 Inner Products
3.2 Orthogonality
3.3 Orthonormal Systems
3.4 Fourier Series
Chapter 4 Linear Operators.Fundamental Theorems
4.1 Bounded Linear Operators and Functionals
4.2 Spaces of Bounded Linear Operators and Dual Spaces
4.3 Banach-Steinhaus Theorem
4.4 Inverses of Operators. Banach's Theorem
4.5 Hahn-Banach Theorem
4.6 Strong and Weak Convergence
Chapter 5 Linear Operators on Hilbert Spaces
5.1 Adjoint Operators. Lax-Milgram Theorem
5.2 Spectral Theorem for Self-adjoint Compact Operators
Chapter 6 Differential Calculus in Normed Linear Spaces
6.1 Gateaux and Frechet Derivatives
6.2 Taylor's Formla, Implicit and Inverse Function Theorems
Bibliography
Index