  We present a brief survey of the results of the Theory of Solitons from the
viewpoint of the periodic theory including some new results in the theory of
2-dimensional periodic Schrodinger Operators. The main subjects are: Periodic
Solitons and Algebraic Geometry, The Theory of Solitons and the String
equation, Topologically trivial and nontrivial periodic two-dimensional
Schrodinger operators and Riemann surfaces and Cyclic and semicyclic chains of
Laplace transformations (new results of the present author and A.Veselov).
