Nonlinear physics is a well-established discipline in physics today, and this book offers a comprehensive account of the basic soliton theory and its applications. Although primarily mathematical, the theory for nonlinear phenomena in practical environments needs to be understood at upper undergraduate level, with particular attention given to the presence of media where nonlinearity takes place. This book addresses mathematical theories, but also suggests possible theoretical innovations for many issues, providing a stimulating reference for both students and researchers.