The contributions to this volume deal with topics ranging over constructive and general quantum field theory and related algebraic problems, non-renormalizable models,equilibrium sta- tistical mechanics, critical phenomena, and nonlinear equations modelling the onset of turbulence. They are based on lectures intended to provide the 1975/1976 research group "Mathematical Problems of Quantum Dynamics" at the Centre for Interdisciplinary Research (ZiF) of Bielefeld University with an input reflecting important recent develop- ments and presented by leading experts in the pertinent fields of research. They further reflect a situation of unusually active and fruit- ful exchange not. only between various specializations of theoretical physics which deal with the specific problems of large systems but also of a lively two-way interaction with mathematics which stimulates and furthers the progress of both disciplines. Thanks are due to the contributors, to the Preparatory Committee - H. Behncke, P. Blanchard, K. Hepp, O. Steinmann, A.S.Wightman -, to the University of Bielefeld for the spon- sorship of these lectures, to the directors and staff of ZiF who made them possible, and to Miss V.C. Fulland and Miss M. Kamper for their calm and competent production of the manuscript.