  We present the deepest optical color-magnitude diagram (CMD) to date of the
local elliptical galaxy M32. We have obtained F435W and F555W photometry based
on HST ACS/HRC images for a region 110" from the center of M32 and a background
field about 320" away from M32 center. Due to the high resolution of our
Nyquist-sampled images, the small photometric errors, and the depth of our data
we obtain the most detailed resolved photometric study of M32 yet.
Deconvolution of HST images proves to be superior than other standard methods
to derive stellar photometry on extremely crowded HST images. The location of
the strong red clump in the CMD suggests a mean age between 8 and 10 Gyr for
[Fe/H] = -0.2 in M32. We detect for the first time a red giant branch bump and
an asymptotic giant branch bump in M32 which indicate that the mean age of
M32's dominant population at ~2' from its center is between 5 and 10 Gyr. We
see evidence of an intermediate-age population in M32 mainly due to the
presence of bright asymptotic giant branch stars. Our detection of a blue
component of stars (blue plume) may indicate for the first time the presence of
a young stellar population, with ages of the order of 0.5 Gyr, in our M32
field. However, it is likely that the brighter stars of this blue plume belong
to the disk of M31 rather than to M32. The fainter stars populating the blue
plume indicate the presence of stars not younger than 1 Gyr and/or blue
straggler stars in M32. M32's dominant population of 8--10 Gyr implies a
formation redshift of 1 < z_f < 2, precisely when observations of the specific
star formation rates and models of "downsizing" imply galaxies of M32's mass
ought to be forming their stars. Our CMD therefore provides a "ground-truth" of
downsizing scenarios at z=0. Our background field data represent the deepest
optical observations yet of the inner disk and bulge of M31. [Abridged]
