Book excerpt: The theory of soliton equations and integrable systems has developed rapidly during the last 20 years with numerous applications in mechanics and physics. For a long time books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this followed one single work by Gardner, Greene, Kruskal, and Miura about the Korteweg-de Vries equation (KdV) which, had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water.