Many physical phenomena are described by partial differential equations which include different scales, one global scale and some local scales. The homogenization theory is a very powerful tool for analyzing problems of this type. The main idea is to approximate the solutions of the original problem by the solution of a so called homogenized equation, which only depends on the global scale. The question is how to find the homogenized equation. During the mathematical analysis of this problem there arise a lot of delicate mathematical problems. The main purpose of this thesis is to collect some of the results and present them as an self contained introduction to the subject.
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