Introduction to the functions on compact Riemann surfaces and theta-functions

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We collect some classical results related to analysis on the Riemann surfaces. The notes may serve as an introduction to the field: we suppose that the reader is familiar only with the basic facts from topology and complex analysis. the treatment is organized to give a background for further applications to non-linear differential equations.
31 pages, lectures given at "First non-orthodox school on Non-linearity and geometry", sept 21-28, 1995, Warsaw

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