  In these lectures we present a general introduction to topological quantum
field theories. These theories are discussed in the framework of the
Mathai-Quillen formalism and in the context of twisted N=2 supersymmetric
theories. We discuss in detail the recent developments in Donaldson-Witten
theory obtained from the application of results based on duality for N=2
supersymmetric Yang-Mills theories. This involves a description of the
computation of Donaldson invariants in terms of Seiberg-Witten invariants.
Generalizations of Donaldson-Witten theory are reviewed, and the structure of
the vacuum expectation values of their observables is analyzed in the context
of duality for the simplest case.
