  This dissertation concerns the classification of groupoid and higher-rank
graph C*-algebras and has two main components. Firstly, for a groupoid it is
shown that the notions of strength of convergence in the orbit space and
measure-theoretic accumulation along the orbits are equivalent ways of
realising multiplicity numbers associated to a sequence of induced
representations of the groupoid C*-algebra. Examples of directed graphs are
given, showing how to determine the multiplicity numbers associated to various
sequences of induced representations of the directed graph C*-algebras.
  The second component of this dissertation uses path groupoids to develop
various characterisations of the C*-algebras of higher-rank graphs. Necessary
and sufficient conditions are developed for the Cuntz-Krieger C*-algebras of
row-finite higher-rank graphs to be liminal and to be postliminal. When Kumjian
and Pask's path groupoid is principal, it is shown precisely when these
C*-algebras have bounded trace, are Fell, and have continuous trace. Necessary
and sufficient conditions are provided for the path groupoids of row-finite
higher-rank graphs without sources to have closed orbits and to have locally
closed orbits. When these path groupoids are principal, necessary and
sufficient conditions are provided for them to be integrable, to be Cartan and
to be proper.
