  We investigate membrane instanton effects in type IIA strings compactified on
rigid Calabi-Yau manifolds. These effects contribute to the low-energy
effective action of the universal hypermultiplet. In the absence of additional
fivebrane instantons, the quaternionic geometry of this hypermultiplet is
determined by solutions of the three-dimensional Toda equation. We construct
solutions describing membrane instantons, and find perfect agreement with the
string theory prediction. In the context of flux compactifications we discuss
how membrane instantons contribute to the scalar potential and the
stabilization of moduli. Finally, we demonstrate the existence of meta-stable
de Sitter vacua.
