  Theta functions play a major role in many current researches and are powerful
tools for studying integrable systems. The purpose of this paper is to provide
a short and quick exposition of some aspects of meromorphic theta functions for
compact Riemann surfaces. The study of theta functions will be done via an
analytical approach using meromorphic functions in the framework of Mumford.
Some interesting examples will be given : the classical Kirchhoff equations in
the cases of Clebsch and Lyapunov-Steklov, the Landau-Lifshitz equation and the
sine-Gordon equation.
