  Gromov-Witten invariants of a symplectic manifold are a count of holomorphic
curves. We describe a formula expressing the GW invariants of a symplectic sum
$X# Y$ in terms of the relative GW invariants of $X$ and $Y$. This formula has
several applications to enumerative geometry. As one application, we obtain new
relations in the cohomology ring of the moduli space of complex structures on a
genus g Riemann surface with n marked points.
