Tilting theory was initiated by Brenner and Butler, see [6] as an explicit generalisation of' Coxeterfunctors' and ' reflection functors' in the sense of [3,9] and 'partial Coxeterfunctors', see [1].In its final form, the notion of a tilting module was introduced and elaborated in [11] by Happel and Ringel; see also [4]. An algebra B is called a tilted algebra if B = End,, (T), where T is a tilting module for some hereditary algebra A.Whereas the category of ^-modules is known if B is representation-finite or A tame, see [17,[266][267] for references and comments, the knowledge is relatively poor in the case of A being wild and B being not of finite type. Apparently the regular v4-modules are the crucial part.Thus in § 1 we deal with regular modules. It was proved in [7] for the incidencealgebra of the r-subspace problem with r ^ 5 and in [2] for any finite-dimensional connected hereditary wild algebra that for non-zero regular modules X and Y there exists an integer N with Horn (X, x l Y) ^ 0 for all / ^ N, r being the Auslander-Reiten translate. We use this statement for the proof of the converse assertion: there exists an integer N' with Hom(A r ,T~'r) = 0 for all / ^ N'.We shall use this result in §2 to treat tilting modules A T without a preprojective, or without a preinjective, direct summand; for example we shall show that in this case the tilted algebra B = End^ (T) is strictly wild provided A is wild.In § § 3 and 4 a reduction algorithm will be introduced which reduces the situation of a general tilting module A T to the case considered in §2. Especially if B is tame, B-mod can be described completely. This concept is illustrated in §5 by several examples.The results of the § §3 and 4 we finally use in the last part to characterise both tame and wild tilted algebras in a way similar to that of Ringel [16, Theorem 2] for tilted algebras of finite type.The paper was written during my stay in Bielefeld. I would like to thank C. M. Ringel for his hospitality, for stimulating discussions and helpful suggestions. Also I would like to thank University Bielefeld and ' Gesellschaft von Freunden und Forderern der Universitat Diisseldorf' for financial support. PreliminariesExcept in §5, where we assume that k is algebraically closed, k always denotes a commutative field. By a A>algebra A we understand a finite-dimensional, basic, associative unitary A>algebra. We write ,4-mod for the category of finitely generated left ,4-modules and the expression module always means finitely generated module.

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