  Building on recent work of Robertson and Steger, we associate a C*-algebra to
a combinatorial object which may be thought of as a higher rank graph. This
C*-algebra is shown to be isomorphic to that of the associated path groupoid.
Sufficient conditions on the higher rank graph are found for the associated
C*-algebra to be simple, purely infinite and AF. Results concerning the
structure of crossed products by certain natural actions of discrete groups are
obtained; a technique for constructing rank 2 graphs from ``commuting'' rank 1
graphs is given.
