0.Introduction
Ⅰ.Algebras and modules
Ⅰ.1.Algebras
Ⅰ.2.Modules
Ⅰ.3.Semisimple modules and the radical of a module
Ⅰ.4.Direct sum decompositions
Ⅰ.5.Projective and injective modules
Ⅰ.6.Basic algebras and embeddings of module categories
Ⅰ.7.Exercises
Ⅱ.Quivers and algebras
Ⅱ.1.Quivers and path algebras
Ⅱ.2.Admissible ideals and quotients of the path algebra
Ⅱ.3.The quiver of a finite dimensional algebra
Ⅱ.4.Exercises
Ⅲ.Representations and modules
Ⅲ.1.Representations of bound quivers
Ⅲ.2.The simple, projective, and injective modules
Ⅲ.3.The dimension Vector of a module and the Euler characteristic
Ⅲ.4.Exercises
Ⅳ.Auslander-Reiten theory
Ⅳ.1.Irreducible morphisms and almost split sequences
Ⅳ.2.The Auslander-Reiten translations
Ⅳ.3.The existence of almost split sequences
Ⅳ.4.The Auslander-Reiten quiver of an algebra
Ⅳ.5.The first Brauer-Thrall conjecture
Ⅳ.6.Functorial approach to almost split sequences
Ⅳ.7.Exercises
Ⅴ.Nakayama algebras and representation-finite group algebras
Ⅴ.1.The Loewy series and the Loewy length of a module
Ⅴ.2.Uniserial modules and right serial algebras
Ⅴ.3.Nakayama algebras
Ⅴ.4.Almost split sequences for Nakayama algebras
Ⅴ.5.Representation-finite group algebras
Ⅴ.6.Exercises
Ⅵ.Tilting theory
Ⅵ.1.Torsion pairs
Ⅵ.2.Partial tilting modules and tilting modules
Ⅵ.3.The tilting theorem of Brenner and Butler
Ⅵ.4.Consequences of the tilting theorem
Ⅵ.5.Separating and splitting tilting modules
Ⅵ.6.Torsion pairs induced by tilting modules
Ⅵ.7.Exercises
Ⅶ.Representation-finite hereditary algebras
Ⅶ.1.Hereditary algebras
Ⅶ.2.The Dynkin and Euclidean graphs
Ⅶ.3.Integral quadratic forms
Ⅶ.4.The quadratic form of a quiver
Ⅶ.5.Reflection functors and Gabriel's theorem
Ⅶ.6.Exercises
ⅤⅢ.Tilted algebras
ⅤⅢ.1.Sections in translation quivers
ⅤⅢ.2.Representation-infinite hereditary algebras
ⅤⅢ.3.Tilted algebras
ⅤⅢ.4.Projectives and injectives in the connecting component
ⅤⅢ.5.The criterion of Liu and Skowronski
ⅤⅢ.6.Exercises
Ⅸ.Directing modules and postprojective components
Ⅸ.1.Directing modules
Ⅸ.2.Sincere directing modules
Ⅸ.3.Representation-directed algebras
Ⅸ.4.The separation condition
Ⅸ.5.Algebras such that all projectives are postprojective
Ⅸ.6.Gentle algebras and tilted algebras of type An
Ⅸ.7.Exercises
A.Appendix.Categories, funetors, and homology
A.1.Categories
A.2.Functors
A.3.The radical of a category
A.4.Homological algebra
A.5.The group of extensions
A.6.Exercises
Bibliography
Index
List of symbols
