Maximal Cohen-Macaulay Modules Over Cohen-Macaulay Rings

The purpose of these notes is to explain in detail some topics on the intersection of commutative algebra, representation theory and singularity theory. They are based on lectures given in Tokyo, but also contain new research. It is the first cohesive account of the area and will provide a useful synthesis of recent research for algebraists. Preliminaries -- Ar Sequences And Irreducible Morphisms -- Isolated Singularities -- Auslander Categories -- Ar Quivers -- The Brauer-thrall Theorem -- Matrix Factorizations -- Simple Singularities -- One-dimensional Cm Rings Of Finite Representation Type -- Mckay Graphs -- Two-dimensional Cm Rings Of Finite Representation Type -- Knörrer's Periodicity -- Grothendieck Groups -- Cm Modules On Quadrics -- Graded Cm Modules On Graded Cm Rings -- Cm Modules On Toric Singularities -- Homogeneous Cm Rings Of Finite Representation Type -- Addenda. Yuji Yoshino. Dedicated To Professor Hideyuki Matsumura On His Sixtieth Birthday. Includes Bibligraphical References (p. 170-173) And Index.