The first volume serves as a general introduction to some of the tech-niques most commonly usedin representation theory. The quiver technique,the Auslander-Reiten theory and the tilting theory were presented withsome application to finite dimensional algebras over a fixed algebraicallydosed field.

Introduction

Ⅹ.Tubes

 Ⅹ.1.Stable tubes

 Ⅹ.2.Standard stable tubes

 Ⅹ.3.Generalised standard components

 Ⅹ.4.Generalised standard stable tubes

 Ⅹ.5.Exercises

Ⅺ.Module categories over concealed algebras of Euclidean type

 Ⅺ.1.The Coxeter matrix and the defect of a hereditary algebra of Euclidean type

 Ⅺ.2.The category of regular modules over a hereditary algebra of Euclidean type

 Ⅺ.3.The category of regular modules over a concealed algebra of Euclidean type

 Ⅺ.4.The category of modules over the Kronecker algebra

 Ⅺ.5.A characterisation of concealed algebras of Euclidean type

 Ⅺ.6.Exercises

Ⅻ.Regular modules and tubes over concealed algebras of Euclidean type

 Ⅻ.1.Canonical algebras of Euclidean type

 Ⅻ.2.Regular modules and tubes over canonical algebras of Euclidean type

 Ⅻ.3.A separating family of tubes over a concealed algebra of Euclidean type

 Ⅻ.4.A controlled property of the Euler form of a concealed algebra of Euclidean type

 Ⅻ.5.Exercises

ⅫⅠ.Indecomposable modules and tubes over hereditary algebras of Euclidean type

 ⅫⅠ.1.Canonically oriented Euclidean quivers, their Coxeter matrices and the defect

 ⅫⅠ.2.Tubes and simple regular modules over hereditary algebras of Euclidean type

 ⅫⅠ.3.Four subspace problem

 ⅫⅠ.4.Exercises

ⅪⅤ. Minimal representation-infinite algebras

 ⅪⅤ.1.Critical integral quadratic forms

 ⅪⅤ.2.Minimal representation-infinite algebras

 ⅪⅤ.3.A criterion for the infinite representation type of algebras

 ⅪⅤ.4.A classification of concealed algebras of Euclidean type

 ⅪⅤ.5.Exercises 

Bibliography

Index

List of symbols