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The present book is the first of its kind in dealing with topological quantum field theories and their applications to topological aspects of four manifolds. It is not only unique for this reason but also because it contains sufficient introductory material that it can be read by mathematicians and theoretical physicists. On the one hand, it contains a chapter dealing with topological aspects of four manifolds, on the other hand it provides a full introduction to supersymmetry. The book constitutes an essential tool for researchers interested in the basics of topological quantum field theory,...

The emergence of topological quantum ?eld theory has been one of the most important breakthroughs which have occurred in the context of ma- ematical physics in the last century, a century characterizedbyindependent developments of the main ideas in both disciplines, physics and mathematics, which has concluded with two decades of strong interaction between them, where physics, as in previous centuries, has acted as a source of new mat- matics. Topological quantum ?eld theories constitute the core of these p- nomena, although the main drivingforce behind it has been the enormous e?ort made in...

During the last three decades supersymmetry has grown into one of the busiest theoretical avenues of particle physics. Supersymmetric ideas dominate the scenario of “beyond the standard model phenomenology”, in spite of the thirty-year-old experimental opacity, a situation that could change within the following decade. One additional important reason for the good health of supersymmetry must be found in the most speculative areas of particle physics. Much of its success comes from superstring theory.The Advanced School on Supersymmetry in the Theories of Fields, Strings and Branes...