  In cohomological field theory we can obtain topological invariants as
correlation functions of BRS cohomology classes. A proper understanding of BRS
cohomology which gives non-trivial results requires the equivariant cohomology
theory. Both topological Yang-Mills theory and topological string theory are
typical examples of this fact. After reviewing the role of the equivariant
cohomology in topological Yang-Mills theory, we show in purely algebraic
framework how the $U(1)$ equivariant cohomology in topological string theory
gives the gravitational descendants. The free energy gives a generating
function of topological correlation functions and leads us to consider a
deformation family of cohomological field theories. In topological strings such
a family is controlled by the theory of integrable system. This is most easily
seen in the Landau-Ginzburg approach by looking at the contact term
interactions between topological observables.
