INTEGRAL QUADRATIC FORMS AND REPRESENTATION TYPES. Jose A. de la Peņa Lecture 1. Three types of bahaviour of path algebras of quivers are distinguished. Examples of local algebras are also given. Definitions of representation types are explained. Dichotomy theorem of Drozd is stated. Lecture 2. The geometric approach of module varieties is described. Voigt theorem and applications are given. Characterization of representation types in geometric terms are provided. Lecture 3. The Tits form of a triangular algebra is introduced. Bongartz' theorem characterizing finite representation is proved. Tame type implies weak non-negativity of the Tits form. Criteria for weak non-negativity of integral unit forms are studied. Critical algebras. Examples are provided. Lecture 4. Separating tubular families are studied and examples given. The values of the Tits form of modules in tubes are calculated. Crawley-Boevey's Theorem claiming that tame algebras have almost all indecomposable on homogeneous tubes is studied. Algebras whose weak non-negativity of the Tits form implies tameness.