  We begin with the construction of Mathai-Quillen's Thom form. We also study
the case with group actions, with a review of equivariant cohomology and then
Mathai-Quillen's construction in this setting. Next, we show that much of the
above can be formulated as a "field theory" on a superspace of one fermionic
dimension. Finally, we present the interpretation of topological field theories
using the Mathai-Quillen formalism.
