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1. Preliminaries 2. AR sequences and irreducible morphisms 3. Isolated singularities 4. Auslander categories 5. AR quivers 6. The Brauer-Thrall theorem 7. Matrix factorizations 8. Simple singularities 9. One-dimensional Cm rings of finite representation type 10. McKay graphs 11. Two-dimensional CM rings of finite representation type 12. Knörrer's periodicity 13. Grothendieck groups 14. CM modules on quadrics 15. Graded CM modules on graded CM rings 16. CM modules on toric singularities 17. Homogeneous CM rings of finite representation type Addenda References.