Aspects of the connections between Path Integrals, Quantum Field Theory, Topology and Geometry

Notes for a mini-course on some aspects of the connections between path integrals, quantum eld theory, topology and geometry, delivered at the XII Fall Workshop on Geometry and Physics, Universidade de Coimbra, September 8{10, 2003. These notes are mostly targeted at geometers with very little or no experience with the Feynman path integral. r