Introduction ⅩⅤ.Tubular extensions and tubular coextensions of algebras ⅩⅤ.1.One-point extensions and one-point coextensions of algebras ⅩⅤ.2.Tubular extensions and tubular coextensions of algebras ⅩⅤ.3.Branch extensions and branch coextensions of algebras ⅩⅤ.4.Tubular extensions and tubular coextensions of concealed algebras of Euclidean type ⅩⅤ.5.Exercises ⅩⅥ.Branch algebras ⅩⅥ.1.Branches and finite line extensions ⅩⅥ.2.Tilted algebras of an equioriented type Am ⅩⅥ.3.Exercises ⅩⅦ.Tilted algebras of Euclidean type ⅩⅦ.1.Stone cones in hereditary standard stable tubes ⅩⅦ.2.Tilting with hereditary standard stable tubes ⅩⅦ.3.Representation-infinite tilted algebras of Euclidean type ⅩⅦ.4.Domestic tubular extensions and domestic tubular coextensions of concealed algebras of Euclidean type ⅩⅦ.5.A classification of tilted algebras of Euclidean type ⅩⅦ.6.A controlled property of the Euler form of tilted algebras of Euclidean type ⅩⅦ.7.Exercises ⅩⅧ.Wild hereditary algebras and tilted algebras of wild type ⅩⅧ.1.Regular components ⅩⅧ.2.Homomorphisms between regular modules ⅩⅧ.3.Perpendicular categories ⅩⅧ.4.Wild behaviour of the module category ⅩⅧ.5.Tilted algebras of wild type ⅩⅧ.6.Exercises ⅪⅩ.Tame and wild representation type of algebras ⅪⅩ.1.Wild representation type ⅪⅩ:2.Indecomposable modules over the polynomial algebra K[t] ⅪⅩ.3.Tame representation type ⅪⅩ.4.Exercises ⅩⅩ.Perspectives ⅩⅩ.1.Components of the Auslander-Reiten quiver of an algebra ⅩⅩ.2.The Tits quadratic form of an algebra ⅩⅩ.3.Tilted and quasitilted algebras ⅩⅩ.4.Algebras of small homological dimensions ⅩⅩ.5.Selfinjective algebras of tilted and quasitilted type ⅩⅩ.6.Related topics and research directions Bibliography Index List of symbols