Selected lectures on nonlinear analysis

This book is written in a corresponding manner that allows an opportunity to use more materials from different fields of mathematics in a brief format. To be exact, the purpose of this book is to present researchers and graduate students with a state-of-the-art survey of some most active areas of nonlinear analysis. The text of the book is fully reflected on CD, which gives an extra flexibility to use the content of the book electronically.The text covers some basic parts of the set theory (Chapter 1), general topology (Chapter 2), functional analysis (Chapter 3), selected topics of nonlinear analysis, including an investigation the problem of local and global solvability of nonlinear operator equations having critical points of different kind (Chapter 4), and some qualitative properties of solutions of nonlinear boundary problems (Chapter 5). A significant part of the book is Appendix 1 where a reader can find some problems' formulation.