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During the week of December 8-13, 1984, a conference on Multi-Grid Methods was held at the Mathematisches Forschungs institut (Mathematical Research Institute) in Oberwolfach. The conference was suggested by the GAMM-Committee "Effiziente numerische Verfahren fUr partielle Differentialgleichungen". We were pleased to have 42 participants from 12 countries. These proceedings contain some contributions to the confe rence. The centre of interest in the more theoretical contri butions were exact convergence proofs for multi-grid method. Here, the theoretical foundation for the application of the method to the Stokes equations, the biharmonic equation in its formulation as a mixed finite element problem and other more involved problems were investigated. Moreover, improvements and new attacks for getting quantitative results on convergence rates were reported. Another series of contributions was concerned with the de velopment of highly efficient and fast algorithms for various partial differential equations. Also in this framework, the Stokes and the biharmonic equations were investigated. Other lectures treated problems from fluid mechanics (as Navier Stokes and Euler equations), the dam-problem and eigenvalue problems. The editors would like to thank Professor M. Barner, the director of Mathematisches Forschungsinstitut Oberwolfach for making this conference possible. D. Braess, Bochum W. Hackbusch, Kiel U. Trottenberg, St. Augustin v CONTENTS O. AXELSSON: A mixed variable finite element method for the efficient solution of nonlinear diffusion and pot- tial flow equations ................................... .