I will introduce relative Seiberg-Witten (or SW) moduli spaces for an arbitrary pair (X,S) of a closed oriented 4-manifold X and a closed oriented 2-dimensional submanifold S in X with positive genus. Using these moduli spaces, we obtain an SW sum formula (aka a product formula) that relates the SW invariants of a sum X of two closed oriented 4-manifolds X1 and X2 along a common oriented surface S with dual self-intersections to the relative SW invariants of (X1,S) and (X2,S). This formula generalizes Morgan-Szabo-Taubes' product formula. This is joint work with Pedram Safari.