  We describe narrowband and spectroscopic searches for emission-line star
forming galaxies in the redshift range 3 to 6 with the 10 m Keck II Telescope.
These searches yield a substantial population of objects with only a single
strong (equivalent width >> 100 Angstrom) emission line, lying in the 4000 -
10,000 Angstrom range. Spectra of the objects found in narrowband-selected
samples at lambda ~5390 Angstroms and ~6741 Angstroms show that these very high
equivalent width emission lines are generally redshifted Lyman alpha 1216
Angstrom at z~3.4 and 4.5. The density of these emitters above the 5 sigma
detection limit of 1.5 e-17 ergs/cm^2/s is roughly 15,000 per square degree per
unit redshift interval at both z~3.4 and 4.5. A complementary deeper (1 sigma
\~1.0 e-18 ergs/cm^2/s) slit spectroscopic search covering a wide redshift
range but a more limited spatial area (200 square arcminutes) shows such
objects can be found over the redshift range 3 to 6, with the currently highest
redshift detected being at z=5.64. The Lyman alpha flux distribution can be
used to estimate a minimum star formation rate in the absence of reddening of
roughly 0.01 solar masses/Mpc^3/year (H_0 = 65 km/s/Mpc and q_0 = 0.5).
Corrections for reddening are likely to be no larger than a factor of two,
since observed equivalent widths are close to the maximum values obtainable
from ionization by a massive star population. Within the still significant
uncertainties, the star formation rate from the Lyman alpha-selected sample is
comparable to that of the color-break-selected samples at z~3, but may
represent an increasing fraction of the total rates at higher redshifts. This
higher-z population can be readily studied with large ground-based telescopes.
