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The Cargese Summer School "Low Dimensional Applications of Quantum Field Theory" was held in July 1995. The School was dedicated to the memory of Claude Itzykson. This session focused on the recent progress in quantum field theory in two dimen- sions with a particular emphasis on integrable models and applications of quantum field theory to condensed matter physics. A large fraction of the school was also devoted to a detailed review of the exciting developments in four dimensional super- symmetric Yang-Mills theory. The diversity of the topics presented constitute, in our opinion, one of the most attractive features of these proceedings. Some contributions constitute a very thor- ough introduction to their subject matter and should be helpful to advanced students in the field while others present entirely new research, not previously published, and should be of considerable interest to the specialist. There were in depth introductory lectures on the application of conformal field theory techniques to disordered systems, on the quantum Hall effect, on quantum in- tegrable systems, on the thermodynamic Bethe Ansatz and on the new developments in supersymmetric gauges theories. The computation of the three point function of the Liouville model using conformal bootstrap methods was presented in detail.