Description The contents of the review include: Perturbation Theory of Finite Zone Solutions of Evolution Lax-type Equations Spectral Theory of Non-Stationary Schrodinger Operators Periodic Problem for Kadomtsev-Petviashvilli-Type Equations Spectral Theory of Two-Dimensional Periodic Schrodinger Operators This review was first published in 1992 and in the course of the last twenty years, these ideas, concepts and methods of the theory of integrable systems have been developed and applied to a wide range of contemporary problems of geometry and topology