  We have obtained spectroscopic redshifts for 24 red galaxies from a sample
with median Ks=18.7 and F814W - Ks > 4, using the Keck telescope. These
EROshave high resolution morphologies from HST (Yan & Thompson 2003). Among the
24 redshifts, the majority (92%) are at $ 0.9 < z < 1.5$. We derived the
rest-frame J-band luminosity function at $z_{median} =1.14$. Our result
suggests that the luminosity evolution between bright EROs at $z\sim 1$ and the
present-day $>$L$^*$ massive galaxies is at most about 0.7 magnitude. Combining
the morphologies and deep spectroscopy revealed the following properties: (1)
86% of the spectra have absorption features from old stars, suggesting that the
dominant stellar populations seen in the rest-frame UV are old stars. 50% of
the sources have pure absorption lines, while the remaining 50% have emission
lines, indicating recent star formation. We conclude that the color criterion
for EROs is very effective in selecting old stellar populations at $z \sim 1$,
and a large fraction of these systems with prominent old stellar populations
also have recent star formation. (2) The 12 emission line systems have the same
number of disk and bulge galaxies as in the remaining 12 pure absorption line
systems. We conclude that spectral classes do not have a simple, direct
correspondence with morphological types. (3) Three EROs could be isolated, pure
passively evolving early-type galaxies at $z\sim 1$. This implies that only a
small fraction (10%--15%) of early-type galaxies are formed in a rapid burst of
star formation at high redshifts and evolved passively since then. (Abridged).
