  This paper studies injective envelopes of groupoid dynamical systems and the
corresponding boundaries. Analogue to the group case, we associate a bundle of
compact Hausdorff spaces to any (discrete) groupoid (the Hamana boundary of the
groupoid). We study bundles of compact topological spaces equipped with an
action of a groupoid. We show that any groupoid has a minimal boundary (the
Furstenberg boundary of the groupoid). We prove that the Hamana and Furstenberg
boundaries are the same, for (discrete) groupoids. We find the relation between
the reduced crossed product of the $\G$-injective envelop of a groupoid
dynamical system and the injective envelope of the reduced crossed product of
the original system.
