The present text reflects developments in the literature on nonlinear systems, while retaining a reader-friendly presentation. It has been developed from problems on nonlinear differential equations given over several years in the nonlinear dynamics team  at the Mechanical Department of Babol Noshirvani University of Technology.  A large variety of applied processes in both linear and nonlinear forms for important nonlinear differential equations are covered, enabling readers to  solve  problems without needing  to refer to other sources.  An introduction to  systems in the context of nonlinear differential equations is provided and is suitable for courses of varying emphasis. The chapters  are designed to be self-contained so readers can easily navigate to the material of interest.  Emphasis is given to direct applications of the subject matter, and will therefore be of particular  interest  to students of engineering, mathematics and the natural sciences.  The most recent analytic methods and developments are included and  over 300 references are given. In addition to discussing  linear and nonlinear problems, demonstrated solutions  are provided.