Cohen Macaulay representations Chapter 1. The Krull Remak Schmidt theorem Chapter 2. Semigroups of modules Chapter 3. Dimension zero Chapter 5. Invariant theory Chapter 6. Kleinian singularities and finite CM type Chapter 7. Isolated singularities and dimension two Chapter 8. The double branched cover Chapter 9. Hypersurfaces with finite CM type Chapter. 10. Ascent and descent Chapter 11. Auslander Buchweitz theory Chapter 12. Totally reflexive modules Chapter 13. Auslander Reiten theory Chapter 14. Countable Cohen Macaulay type Chapter 15. The Brauer Thrall conjectures Chapter 16. Finite CM type in higher dimensions Chapter 17. Bounded CM type Appendix A. Basics and background Appendix B. Ramification theory