  We define relative Gromov-Witten invariants of a symplectic manifold relative
to a codimension two symplectic submanifold. These invariants are the key
ingredients in the symplectic sum formula of [IP4]. The main step is the
construction of a compact space of `V-stable' maps. Simple special cases
include the Hurwitz numbers for algebraic curves and the enumerative invariants
of Caporaso and Harris.
