This book contains thoroughly written reviews of modern developments in low-dimensional modelling of statistical mechanics and quantum systems. It addresses students as well as researchers. The main items can be grouped into integrable (quantum) spin systems, which lead in the continuum limit to (conformal invariant) quantum field theory models and their algebraic structures, ranging from the Yang-Baxter equation and quantum groups to noncommutative geometry.

This volume contains the written versions of invited lectures and abstracts of seminars presented at the 26th "Universitatswochen fiir Kernphysik" (Uni versity nuclear physics weeks) in Schladming, Austria, in February 1987. Again the generous support of our sponsors, the Austrian Ministry of Sci ence and Research, the Styrian government and others, made it possible to invite expert lecturers. The meeting was organized in honour of Prof. Dr. th Walter Thirring in connection with his 60 birthday. In choosing the topics for the lectures we have tried to cover a good many of the areas in which mathematical physics has made significant progress in recent years. Both classical and quantum mechanical problems are considered as well as prob lems in statistical physics and quantum field theory. The common feature lies in the methods of mathematical physics that are used to understand the underlying structure and to proceed towards a rigorous solution. Thanks to the efforts of the speakers this spirit was maintained in all lectures. Due to space limitations only shortened versions of the many seminars presented in Schladming could be included. After the school the lecture notes were revised by the authors, whom we thank for their efforts, which made it possible to speed up publication. Thanks are also due to Mrs. Neuhold for the careful typing of the notes, and to Miss Koubek and Mr. Preitler for their help in proofreading."