  We propose a general theory of the Open Gromov-Witten invariant on Calabi-Yau
three-folds. We introduce the moduli space of multi-curves and show how it
leads to invariants. Our construction is based on an idea of Witten.
  In the special case that each connected component of the Lagrangian
submanifold has the rational homology of a sphere we define rational numbers
$F_{g,h}$ for each genus $g$ and $h$ boundary components.
