  These lecture notes give an introductory account of an approach to
cohomological field theory due to Atiyah and Jeffrey which is based on the
construction of Gaussian shaped Thom forms by Mathai and Quillen. Topics
covered are: an explanation of the Mathai-Quillen formalism for finite
dimensional vector bundles; the definition of regularized Euler numbers of
infinite dimensional vector bundles; interpretation of supersymmetric quantum
mechanics as the regularized Euler number of loop space; the Atiyah-Jeffrey
interpretation of Donaldson theory; the construction of topological gauge
theories from infinite dimensional vector bundles over spaces of connections.
