  We study the path integral of a twisted $N=2$ supersymmetric Yang-Mills
theory coupled with hypermultiplet having the bare mass. We explicitly compute
the topological correlation functions for the $SU(2)$ theory on a compact
oriented simply connected simple type Riemann manifold with $b_2^+ \geq 3$. As
the corollaries, we determine the topological correlation functions of the
theory without the bare mass and those of the theory without coupling to the
hypermultiplet. This includes a concrete field theoretic proof of the relation
between the Donaldson and the Seiberg-Witten invariants.
