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| Introduction | |
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| Algebras and modules | |
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| Algebras | |
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| Modules | |
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| Semisimple modules and the radical of a module | |
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| Direct sum decompositions | |
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| Projective and injective modules | |
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| Basic algebras and embeddings of module categories | |
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| Exercises | |
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| Quivers and algebras | |
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| Quivers and path algebras | |
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| Admissible ideals and quotients of the path algebra | |
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| The quiver of a finite dimensional algebra | |
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| Exercises | |
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| Representations and modules | |
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| Representations of bound quivers | |
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| The simple, projective, and injective modules | |
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| The dimension vector of a module and the Euler characteristic | |
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| Exercises | |
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| Auslander-Reiten theory | |
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| Irreducible morphisms and almost split sequences | |
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| The Auslander-Reiten translations | |
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| The existence of almost split sequences | |
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| The Auslander-Reiten quiver of an algebra | |
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| The first Brauer-Thrall conjecture | |
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| Functorial approach to almost split sequences | |
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| Exercises | |
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| Nakayama algebras and representation-finite group algebras | |
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| The Loewy series and the Loewy length of a module | |
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| Uniserial modules and right serial algebras | |
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| Nakayama algebras | |
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| Almost split sequences for Nakayama algebras | |
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| Representation-finite group algebras | |
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| Exercises | |
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| Tilting theory | |
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| Torsion pairs | |
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| Partial tilting modules and tilting modules | |
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| The tilting theorem of Brenner and Butler | |
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| Consequences of the tilting theorem | |
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| Separating and splitting tilting modules | |
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| Torsion pairs induced by tilting modules | |
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| Exercises | |
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| Representation-finite hereditary algebras | |
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| Hereditary algebras | |
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| The Dynkin and Euclidean graphs | |
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| Integral quadratic forms | |
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| The quadratic form of a quiver | |
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| Reflection functors and Gabriel's theorem | |
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| Exercises | |
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| Tilted algebras | |
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| Sections in translation quivers | |
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| Representation-infinite hereditary algebras | |
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| Tilted algebras | |
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| Projectives and injectives in the connecting component | |
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| The criterion of Liu and Skowronski | |
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| Exercises | |
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| Directing modules and postprojective components | |
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| Directing modules | |
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| Sincere directing modules | |
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| Representation-directed algebras | |
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| The separation condition | |
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| Algebras such that all projectives are postprojective | |
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| Gentle algebras and tilted algebras of type A[subscript n] | |
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| Exercises | |
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| Categories, functors, and homology | |
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| Categories | |
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| Functors | |
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| The radical of a category | |
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| Homological algebra | |
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| The group of extensions | |
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| Exercises | |
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| Bibliography | |
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| Index | |
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| List of symbols | |