Nonlinear Physics is a well-established discipline of physics today, for which this book offers a comprehensive account of the basic soliton theory and its applications. Although primarily mathematical, the author discusses the theory for nonlinear phenomena in practical environment to be understood with knowledge at upper undergraduate level, paying particular attention to the presence of media where nonlinearity takes place. This book addresses the mathematical theory with respect to the past development, however implies possible theoretical innovations on many issues, providing a stimulating reference for students and researchers.