  We present a complete morphologically classified sample of 144 faint field
galaxies from the HST Medium Deep Survey with 20.0 < I <22.0 mag. We compare
the global properties of the ellipticals, early and late-type spirals, and find
a non-negligible fraction (13/144) of compact blue [(V-I) < 1.0 mag] systems
with $r^{1/4}$-profiles. We give the differential galaxy number counts for
ellipticals and early-type spirals independently, and find that the data are
consistent with no-evolution predictions based on conventional flat Schechter
luminosity functions (LF's) and a standard cosmology.
  Conversely, late-type/Irregulars show a steeply rising differential number
count with slope $(\frac{\delta log N}{\delta m}) = 0.64\pm 0.1$. No-evolution
models based on the Loveday et al. (1992) and Marzke et al. (1994b) {\it local}
luminosity functions under-predict the late-type/Irregular counts by 1.0 and
0.5 dex, respectively, at I = 21.75 mag. Examination of the Irregulars alone
shows that $\sim 50$% appear inert and the remainder have multiple cores. If
the inert galaxies represent a non-evolving late-type population, then a
Loveday-like LF ($\alpha\simeq -1.0$) is ruled out for these types, and a LF
with a steep faint-end ($\alpha\simeq -1.5$) is suggested. If multiple core
structure indicates recent star-formation, then the observed excess of faint
blue field galaxies is likely due to {\it evolutionary} processes acting on a
{\it steep} field LF for late-type/Irregulars. The evolutionary mechanism is
unclear, but 60% of the multiple-core Irregulars show close companions. To
reconcile a Marzke-like LF with the faint redshift surveys, this evolution must
be preferentially occurring in the brightest late-type galaxies with z > 0.5 at
I = 21.75 mag.
