  We discuss questions of isospectrality for hyperbolic orbisurfaces, examining
the relationship between the geometry of an orbisurface and its Laplace
spectrum. We show that certain hyperbolic orbisurfaces cannot be isospectral,
where the obstructions involve the number of singular points and genera of our
orbisurfaces. Using a version of the Selberg Trace Formula for hyperbolic
orbisurfaces, we show that the Laplace spectrum determines the length spectrum
and the orders of the singular points, up to finitely many possibilities.
Conversely, knowledge of the length spectrum and the orders of the singular
points determines the Laplace spectrum. This partial generalization of Huber's
theorem is used to prove that isospectral sets of hyperbolic orbisurfaces have
finite cardinality, generalizing a result of McKean for Riemann surfaces.
