  In this paper, we demonstrate a relation among Seiberg-Witten invariants
which arises from embedded surfaces in four-manifolds whose self-intersection
number is negative. These relations, together with Taubes' basic theorems on
the Seiberg-Witten invariants of symplectic manifolds, are then used to prove
the symplectic Thom conjecture: a symplectic surface in a symplectic
four-manifold is genus-minimizing in its homology class. Another corollary of
the relations is a general adjunction inequality for embedded surfaces of
negative self-intersection in four-manifolds.
