For any smooth complex projective variety $X$ and any smooth very
ample hypersurface $Y\subset X$, we develop the technique of genus
zero relative Gromov-Witten invariants of $Y$ in $X$ in
algebro-geometric terms. We prove an equality of cycles in the Chow
groups of the moduli spaces of relative stable maps which relates
these relative invariants to the Gromov-Witten invariants of $X$ and
$Y$. Given the Gromov-Witten invariants of $X$, we show that these
relations are sufficient to compute all relative invariants, as well
as all genus zero Gromov-Witten invariants of $Y$ whose homology and
cohomology classes are induced by $X$.