TQFT, the acronym for Topological Quantum Field Theory, is a construction which arose in physics, but has found applications in several areas of mathematics, in particular the theory of knots, braids and similar objects. The purpose of this talk is to explain some of the underlying notions, in such a way as to be accessible to people with a wide range of mathematical backgrounds. If time allows I will describe a geometric application: parallel transport for bundles and gerbes.