We present 10 m Keck spectroscopy and photometry for a sample of 61 sm
all (r(1/2) less than or equal to 0''.5), faint (I-814 less than or eq
ual to 23.74), high-surface brightness (mu(I814) < 22.2 mag arcsec(-2)
) galaxies in fields flanking the Hubble Deep Field. The majority of t
his empirically defined sample of compact galaxies lies at redshifts 0
.4 less than or similar to z less than or similar to 1 (88% completene
ss in redshift identifications), ruling out a large component of low-r
edshift galaxies. The number of such galaxies in the range 1.4 less th
an or similar to z less than or similar to 2.2 is also constrained to
less than or similar to 10%. The majority of the observed galaxies are
emission-line systems, while a significant fraction (23%-34%) appear
to be normal ellipticals or otherwise early-type systems. One object i
s an active galactic nucleus, and two are at high redshift (z > 2). Th
e Keck redshift and photometric data are combined with Hubble Space Te
lescope images to derive luminosities and physical sizes. We also use
emission-line widths, where available, to estimate masses. About two-t
hirds of the emission-line galaxies, or roughly one-half the sample, a
re small, low-mass, relatively luminous systems with properties resemb
ling those of local H II galaxies. We compare the properties and numbe
rs of these galaxies to the ''bursting dwarf'' model of Babul & Fergus
on. Our sample includes many galaxies similar to the model galaxies in
the redshift range 0.4 less than or similar to z less than or similar
to 0.7, but the majority of our compact galaxies are more luminous (b
y up to an order of magnitude) than those of the model. The number of
galaxies fitting the model parameters are lower by a factor of 2-3 tha
n predicted. An examination of samples used in analyses of disk surfac
e brightness at redshifts z > 0.5 shows that compact galaxies are like
ly to contribute to the strong disk luminosity evolution found in some
studies. Estimates of comoving volume densities indicate that the pop
ulation of apparent H II galaxies evolves rapidly from redshifts of z
similar to 1 to the present. It appears that not all of these galaxies
can be progenitors of present-day spheroidal galaxies, although the n
umbers of them with sizes and masses comparable to spheroidals is not
dissimilar to estimates of the local field spheroidal density. We also
present 51 additional redshifts, acquired for other projects during t
he same observing period, for a total of 105 objects with identified r
edshifts z < 2 in the Hubble Deep Field and its flanking fields.