This second part of the monograph on soliton equations contains a continuation of a systematic description of properties of solutions for hierarchies of soliton equations using methods from algebraic geometry. This volume is devoted to equations with one continuous (time) variable and one discrete (space) variable. There are three main examples treated in the book: the Toda hierarchy, the Kac-van Moerbeke hierarchy and the Ablowitz-Ladik hierarchy. The appendices collect together some preliminary material on algebraic curves (hyperelliptic, in particular), spectral parameter expansions and Lagrange interpolation. As with the first part, the book is very well-written and carefully organized and it is a pleasure to read it. It can be recommended to all readers interested in the topic.