In this book, the basic methods of nonlinear analysis are emphasized and illustrated in simple examples. Every considered method is motivated, explained in a general form but in the simplest possible abstract framework. Its applications are shown, particularly to boundary value problems for elementary ordinary or partial differential equations. The text is organized in two levels: a self-contained basic and, organized in appendices, an advanced level for the more experienced reader. Exercises are an organic part of the exposition and accompany the reader throughout the book. It is an ideal textbook for advanced undergraduate and graduate students as well as a useful handbook of nonlinear methods for scientists and engineers.

Preliminaries.- Properties of Linear and Nonlinear Operators.- Abstract Integral and Differential Calculus.- Local Properties of Differentiable Mappings.- Topological and Monotonicity Methods.- Variational Methods.- Boundary Value Problems for Partial Differential Equations.