The emergence of topological quantum field 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 field theories constitute the core of these p- nomena, although the main drivingforce behind it has been the enormous effort made in theoretical particle physics to understand string theory as a theory able to unify the four fundamental interactions observed in nature. These theories set up a new realm where both disciplines profit from each other. Although the most striking results have appeared on the mathema- calside, theoretical physics has clearly also benefitted, since the corresponding developments have helped better to understand aspects of the fundamentals of field and string theory.