The second edition of this popular book on nonlinear wave dynamics closely follows the first edition [for the review see (1990; Zbl 0726.76018)] and therefore reflects the state of research in the early 1990’s. The authors added several examples from nonlinear optics, biology, solid state physics and other fields, and some new results and references. There is a new chapter 10 on soliton metamorphosis, where the authors describe the evolution of instabilities for one- and two-dimensional solitons in two- and three-dimensional space.