Planetary camera observations of the central parsec of M32

New HST observations are reported which show that the M32 nucleus is extremely dense, with rho0 not less than 4 x 10 exp 6 solar masses/cu pc if M32 has a core with rc not greater than 0.37 pc, and rho0 greater than 3 x 10 exp 7 solar masses/cu pc if it instead has a central r exp -1/2 cusp. Limits on the M32 core radius are nearly three times smaller, and those on the central density at least four times greater, than values inferred from the best ground-based observations. A central relaxation that is almost an order of magnitude shorter than previous estimates is inferred from the new core parameters; a shorter stellar collision time is also inferred. It is argued that a starlight cusp surrounds the central black hole.