  We present results from modeling the optical spectra of a large sample of
quiescent galaxies between 0.1 < z < 0.7 from the Sloan Digital Sky Survey
(SDSS) and the AGN and Galaxy Evolution Survey (AGES). We examine how the
stellar ages and abundance patterns of galaxies evolve over time as a function
of stellar mass from 10^{9.6}-10^{11.8} Msun. Galaxy spectra are stacked in
bins of mass and redshift, and modeled over a wavelength range from 4000 A to
5500 A. Full spectrum stellar population synthesis modeling provides estimates
of the age and the abundances of the elements Fe, Mg, C, N, and Ca. We find
negligible evolution in elemental abundances at fixed stellar mass over roughly
7 Gyr of cosmic time. In addition, the increase in stellar ages with time for
massive galaxies is consistent with passive evolution since z = 0.7. Taken
together, these results favor a scenario in which the inner ~ 0.3-3 R_e of
massive quiescent galaxies have been passively evolving over the last half of
cosmic time. Interestingly, the derived stellar ages are considerably younger
than the age of the universe at all epochs, consistent with an equivalent
single-burst star formation epoch of z < 1.5. These young stellar population
ages coupled with the existence of massive quiescent galaxies at z > 1 indicate
the inhomogeneous nature of the z < 0.7 quiescent population. The data also
permit the addition of newly-quenched galaxies at masses below ~10^{10.5} Msun
at z < 0.7. Additionally, we analyze very deep Keck DEIMOS spectra of the two
brightest quiescent galaxies in a cluster at z = 0.83. There is tentative
evidence that these galaxies are older than their counterparts in low-density
environments. In the Appendix, we demonstrate that our full spectrum modeling
technique allows for accurate and reliable modeling of galaxy spectra to low
S/N (~20 A^{-1}) and/or low spectral resolution (R ~ 500).
