  Just as $\Cstar$ principal bundles provide a geometric realisation of
two-dimensional integral cohomology; gerbes or sheaves of groupoids, provide a
geometric realisation of three dimensional integral cohomology through their
Dixmier-Douady class. I consider an alternative, related, geometric realisation
of three dimensional cohomology called a bundle gerbe. Every bundle gerbe gives
rise to a gerbe and most of the well-known examples examples of gerbes are
bundle gerbes. I discuss the properties of bundle gerbes, in particular bundle
gerbe connections and curvature and their associated Dixmier-Douady class.
