  We present a number of findings concerning groupoid dynamical systems and
groupoid crossed products. The primary result is an identification of the
spectrum of the groupoid crossed product when the groupoid has continuously
varying abelian stabilizers and a well behaved orbit space. In this case, the
spectrum of the crossed product is homeomorphic, via an induction map, to a
quotient of the spectrum of the crossed product by the stabilizer group bundle.
The main theorem is also generalized in the groupoid algebra case to an
identification of the primitive ideal space. This generalization replaces the
assumption that the orbit space is well behaved with an amenability hypothesis.
We then use induction to show that the primitive ideal space of the groupoid
algebra is homeomorphic to a quotient of the dual of the stabilizer group
bundle. In both cases the identification is topological. We then apply these
theorems in a number of examples, and examine when a groupoid algebra has
Hausdorff spectrum. As a separate result, we also develop a theory of principal
groupoid group bundles and locally unitary groupoid actions. We prove that such
actions are characterized, up to exterior equivalence, by a cohomology class
which arises from a principal bundle. Furthermore, we also demonstrate how to
construct a locally unitary action from a given principal bundle. This last
result uses a duality theorem for abelian group bundles which is also included
as part of this thesis.
