A joint research project of algebraists from the universities of Antwerp, Biele- feld, Essen, Leeds, Paris VI and Trondheim on Invariants and Representations of Algebras has been supported from 1991 to 1997 by the European Union programmes Science and Human Capital and Mobility , it was coordinated by Mme M. -P. Malliavin (Paris VI). Later, algebraists from the universities of Edinburgh, Ioannina, Murcia and Torun joined the collaboration. This network is now coordinated by C. M. Ringel (Bielefeld). It has received funds from the European Commission in order to organize four conferences as part of the pro- gramme Training and Mobility of Researchers , to be held during the period 1997-1999 at Essen, Murcia, Bielefeld and Ioannina. The first Euroconference of this series took place at the University of Essen, April 1-4, 1997. It was devoted to Computational Methods for Representations of Groups and Algebras . The organizers were P. Draxler (Bielefeld) and G. Michler (Essen). This volume collects most of the material presented at the conference. There had been an additional introductory lecture by H. Gollan; it is not included here, since its contents is available in the lecture notes: P. Fleischmann, G. O. Michler, P. Roelse, J. Rosenboom, R. Staszewski, C. Wagner, M. Weller, Linear algebra over small finite fields on parallel machines , Vorlesungen Fachbereich Math. Univ. Essen, 23 (1995). Together with these notes, this volume will provide a survey on the present state of art.