  We report on a large HST imaging survey of BL Lac objects, at spatial
resolution ~10 times better than previous ground-based surveys. We focus on
data reduction and analysis, describing the procedures used to model the host
galaxy surface brightness radial profiles. A total of 69 host galaxies were
resolved out of 110 objects observed, including almost all sources at z < 0.5.
We classify them morphologically by fitting with either an exponential disk or
a de~Vaucouleurs profile; when one fit is preferred over the other, in 58 of 69
cases, it is invariably the elliptical morphology. This is a very strong result
given the large number of BL Lac objects, the unprecedented spatial resolution,
and the homogeneity of the data set. With the present reclassification of the
host galaxy of 1418+546 as an elliptical, there remain no undisputed examples
of a disk galaxy hosting a BL Lac nucleus. This implies that, at 99%
confidence, fewer than 7% of BL Lacs can be in disk galaxies. The apparent
magnitude of the host galaxies varies with distance as expected if the absolute
magnitudes are approximately the same, with a spread of +-1 mag, out to
redshift z < 0.5. At larger redshifts, only 6 of 23 BL Lacs are resolved so the
present data do not constrain possible luminosity evolution of the host
galaxies. The collective Hubble diagram for BL Lac host galaxies and radio
galaxies strongly supports their unification.
