On covering theory and its applications

The aim of this survey is to present applications of covering techniques in the theory of Krull-Gabriel dimension. We start with recalling fundamental facts of the classical covering theory of quivers and locally bounded categories. Then we present some recent results on covering theory of functor categories. These are interesting themselves, but also allow to relate Krull-Gabriel dimensions of locally bounded categories $R$ and $A$ when $R\rightarrow A$ is a Galois covering functor. Finally, we concentrate on applications of our methods in describing Krull-Gabriel dimensions of various classes of algebras and locally bounded categories.