Nonlinear physics today is a well established discipline of physics, for which this book offers a comprehensive account of soliton theory and its applications. Primarily mathematical though, the author discusses the theory in the physical environment for readers’ precise understanding. Particular emphasis is placed on the presence of media, which is responsible for nonlinearity of propagating waves, depending on environmental conditions. Designed as a textbook for use in advanced physics courses, Introduction to the Mathematical Physics of Nonlinear Waves is readable with a knowledge of physics and mathematics at undergraduate level.