We have analysed archival {it ROSAT} PSPC data for M32 in order to study the x-ray emission from this nearest elliptical galaxy. We fit spectra from three long exposures with Raymond-Smith, thermal bremsstrahlung, and power-law models. All models give excellent fits. The thermal fits have kT$approx$4 keV, the Raymond-Smith iron abundance is $0.4^{+0.7}_{-0.3}$ Solar, the power-law fit has $alpha$=1.6$pm$0.1, and all fits have $N_H$ consistent with the Galactic column. The source is centered on M32 to an accuracy of 9$$, and unresolved at 27$$ FWHM ($sim$90 pc). M32 is x-ray variable by a factor of 3--5 on timescales of a decade down to minutes, with evidence for a possible period of $sim$1.3 days. There are two plausible interpretations for these results: 1) Emission due to low-mass x-ray binaries; 2) Emission due to accretion onto a massive central black hole. Both of these possibilities are supported by arguments based on previous studies of M32 and other old stellar systems; the {it ROSAT} PSPC data do not allow us to unambiguously choose between them. Observations with the {it ROSAT} HRI and with {it ASCA} are required to determine which of these two very different physical models is correct.
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