  The Hubble Deep Field (HDF) is the deepest set of multicolor optical
photometric observations ever undertaken, and offers a valuable data set with
which to study galaxy evolution. Combining the optical WFPC2 data with
ground-based near-infrared photometry, we derive photometrically estimated
redshifts for HDF galaxies with J<23.5. We demonstrate that incorporating the
near-infrared data reduces the uncertainty in the estimated redshifts by
approximately 40% and is required to remove systematic uncertainties within the
redshift range 1<z<2. Utilizing these photometric redshifts, we determine the
evolution of the comoving ultraviolet (2800 A) luminosity density (presumed to
be proportional to the global star formation rate) from a redshift of z=0.5 to
z=2. We find that the global star formation rate increases rapidly with
redshift, rising by a factor of 12 from a redshift of zero to a peak at z~1.5.
For redshifts beyond 1.5, it decreases monotonically. Our measures of the star
formation rate are consistent with those found by Lilly et al. (1996) from the
CFRS at z<1, and by Madau et al. (1996) from Lyman break galaxies at z > 2, and
bridge the redshift gap between those two samples. The overall star formation
or metal enrichment rate history is consistent with the predictions of Pei and
Fall (1995) based on the evolving HI content of Lyman-alpha QSO absorption line
systems.
