Cohen-Macaulay modules over simple singularities

The thesis is focused on the maximal Cohen-Macaulay modules over simple singular- ities. Previous results on the topic are summarised, and in particular it is shown that a hypersurface is MCM-finite if and only if it is a simple singularity. The stable Auslander- Reiten quivers of simple singularities are drawn for better understanding of the category of maximal Cohen-Macaulay modules over a simple singularity.