本书研究的主题涵盖了非线性分析的大部分内容，共分为五部分：第一部分介绍了函数空间；第二部分给出了非线性和多值映射的相关内容；第三部分阐述了光滑与非光滑微积分的相关理论；第四部分论述了拓扑度理论和不动点理论；第五部分介绍了变分和拓扑方法，不仅给出了相关的定义和结果，还阐述了有关概念和结果的注释和评论，约有200个问题及其解决方案，可以帮助读者在解决问题之前掌握其理论知识。本书适合大学师生及数学爱好者参考阅读。

1 Function Spaces
1.1 Introduction
1.1.1 LP-Spaces
1.1.2 Lebesgue-Bochner Spaces
1.1.3 BUFunctions.Absolutely Continuous Functions Spaces of Measures
1.1.4 Sobolev Spaces
1.1.5 Auxiliary Notions
1.2 Problems
1.3 Solutions
Bibliography
2 Nonlinear and Multivalued Maps
2.1 Introduction
2.1.1 Compact，Completely Continuous，and Proper Maps
2.1.2 Multifunctions
2.1.3 Maximal Monotone Maps and Generalizations
2.1.4 Accretive Maps
2.1.5 Miscellaneous Results
2.2 Problems
2.3 Solutions
Bibliography
3 Smooth and Nonsmooth Calculus
3.1 Introduction
3.1.1 Ggteaux and Pr6chet Derivatives
3.1.2 Convex Functionals and Variational Inequalities
3.1.3 Locally Lipschitz Functions
3.1.4 г一Convergence and Relaxation
3.2 Problems
3.3 Solutions
Bibliography
4 Degree Theory and Fixed Point Theory
4.1 Introduction
4.1.1 Degree Theory
4.1.2 Metric Fixed Point Theory
4.1.3 Topological Fixed Point Theory
4.1.4 Order Fixed Point Theory
4.2 Problems
4.3 Solutions
Bibliography
5 Variational and Topological Methods
5.1 IIltroduction
5.1.1 Minimization Methods
5.1.2 Minimax Methods for Critical Points
5.1.3 Morse Theory：Critical Groups
5.1.4 Dirichlet Elliptic Problems
5.2 Problems
5.3 Solutions
Bibliography
List of Symbols
Index
编辑手记