The purpose of this book is to provide research workers in applied mathematics, physics and engineering with practical methods for solving systems of nonlinear partial differential equations. The first two chapters provide an introduction to the more or less classical results of Lie dealing with symmetries and similarity solutions. The results, however, are presented in the context of a contact manifold rather than the usual jet bundle formulation and provide a number of new conclusions. The remaining three chapters present essentially new methods of solution that are based on recent...