The present book is based on a one semester course at the University of Craiova. The goal of this textbook is to provide the background which is necessary to initiate work on a Ph.D. thesis in Applied Nonlinear Analysis. My purpose is to provide for the student a broad perspective in the subject, to illustrate the rich variety of phenomena encompassed by it and to impart a working knowledge of the most important techniques of analysis of the solutions of the equations. The level of this book is aimed at beginning graduate students. Prerequisites include a truly advanced Calculus course, basic knowledge on Functional Analysis and PDE, as well as the necessary tools on Sobolev spaces.