  We have obtained spectra through small apertures centered on the nuclear
region and major axis of M32, with the HST/FOS. A detailed analysis and
reduction of the data is presented, including: (i) new calibrations and
modeling of the FOS aperture sizes, PSF and line-spread-functions; (ii)
determination of the aperture positioning for each observation; and (iii)
accurate wavelength calibration, template matching, and kinematical analysis of
the spectra. This yields measurements of the stellar rotation velocities and
velocity dispersions with five times higher spatial resolution than the best
available ground-based data. The inferred velocities provide the highest
angular resolution stellar kinematical data obtained to date for any stellar
system.
  The observations show a steeper rotation curve and higher central velocity
dispersion than ground-based data. The rotation velocity is observed to be 30
km/s at 0.1" from the nucleus; roughly twice the value measured from the ground
at this distance. The nuclear dispersion measured through the smallest FOS
aperture (0.068" square) is 156 +/- 10 km/s. The average of four independent
dispersion measurements at various positions inside the central 0.1" is 126
km/s, with a RMS scatter of 21 km/s. The nuclear dispersion measured from the
ground is only 85-95 km/s, whereas the dispersion outside the central arcsec is
only 45-55 km/s. These results significantly strengthen previous arguments for
the presence of a massive nuclear black hole in M32. Detailed dynamical models
are presented in a series of companion papers.
