This self-contained, comprehensive handbook provides an in-depth examination of important theoretical methods and procedures in applied analysis. Presents an accessible introduction to modern analysis, while still serving as a useful reference for researchers and practitioners. Covers a large number of diverse topics: smooth and nonsmooth differential calculus, optimal control, fixed point theory, critical point theory, linear and nonlinear eigenvalue problems, nonlinear boundary value problems, set-valued analysis, game theory, stochastic analysis, and evolutionary equations.Serves as a complete guide to the theory of nonlinear analysis;Includes numerous examples that demonstrate and expand upon the topics presented; ?