  Etale groupoids arise naturally as models for leaf spaces of foliations, for
orbifolds, and for orbit spaces of discrete group actions. In this paper we
introduce a sheaf homology theory for etale groupoids. We prove its invariance
under Morita equivalence, as well as Verdier duality between Haefliger
cohomology and this homology. We also discuss the relation to the cyclic and
Hochschild homologies of Connes' convolution algebra of the groupoid, and
derive some spectral sequences which serve as a tool for the computation of
these homologies.
