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This book is an introduction to the contemporary representation theory of Artin algebras, by three very distinguished practitioners in the field. Beyond assuming some first-year graduate algebra and basic homological algebra, the presentation is entirely self-contained, so the book is a suitable introduction for any mathematician (especially graduate students) to this field. The main aim of the book is to illustrate how the theory of almost split sequences is used in the representation theory of Artin algebras. However, other foundational aspects of the subject are developed. These results give concrete illustrations of some of the more abstract concepts and theorems. The book includes complete proofs of all theorems, and numerous exercises.

Artin rings. --- Artin algebras. --- Representations of algebras.

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Ordered algebraic structures --- Graded rings. --- Artin algebras. --- Koszul algebras. --- Duality theory (Mathematics) --- Anneaux gradués. --- Algèbres artiniennes. --- Algèbres de Koszul. --- Dualité, Principe de (mathématiques) --- Artin algebras --- Graded rings --- Koszul algebras --- Algebras, Artin --- Artin rings --- Commutative algebra --- Modules (Algebra) --- Associative algebras --- Rings (Algebra) --- Algebra --- Mathematical analysis --- Topology

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Artin algebras --- Partially ordered sets. --- Commutative algebra. --- Algèbres artiniennes --- Ensembles partiellement ordonnés --- Algèbre commutative --- Artin algebras. --- Algèbres artiniennes --- Ensembles partiellement ordonnés --- Algèbre commutative --- Algebra --- Commutative algebra --- Partially ordered sets --- 51 <082.1> --- Posets --- Sets, Partially ordered --- Ordered sets --- Algebras, Artin --- Artin rings --- Modules (Algebra) --- Mathematics--Series