  Axisymmetric dynamical models are constructed for the E3 galaxy M32 to
interpret high spatial resolution stellar kinematical HST data. Models are
studied with two-integral phase-space distribution functions, and with fully
general three- integral distribution functions. The latter are built using a
new extension of Schwarzschild's orbit superposition approach. Models are
constructed for inclinations of 90 and 55 degrees. No model without a nuclear
dark object can fit the combined ground-based and HST data, independent of the
dynamical structure of M32. Models with a nuclear dark object of 3.4 x 10^6
solar masses do provide an excellent fit. The inclined models provide the best
fit, but the inferred dark mass does not depend sensitively on the assumed
inclination. The models that best fit the data are not two-integral models, but
like two-integral models they are azimuthally anisotropic. An extended dark
object can fit the data only if its half-mass radius is r_h < 0.08 arcsec
(=0.26 pc), implying a central dark matter density exceeding 1 x 10^8 solar
masses / pc^3. This density is high enough to rule out most plausible
alternatives to a massive black hole. The dynamically inferred dark mass is
identical to that suggested by existing adiabatic black hole growth models for
HST photometry of M32. The low activity of M32 implies either that only a very
small fraction of the gas that is shed by evolving stars is accreted onto the
black hole, or that accretion proceeds at very low efficiency, e.g. in an
advection-dominated mode. (shortened version)
