Geometric and Topological Methods for Quantum Field Theory, Proceedings of the Summer School Villa de Leyva, Colombia 9 - 27 july 2001

This volume introduces some mathematical and physical tools and methods required to follow the recent developments, and provides insight in various active areas of mathematical physics, including duality, gauge field theory, conformal field theory, topological field theory, noncommutative geometry, and geometry of low-dimensional manifolds. It comprises seven self-contained lectures, which should progressively give the reader a precise idea of some of the techniques used in these areas, as well as a few short communications presented by young participants at the school and two appendices recalling some basic notions in differential geometry and quantum field theory.