We study the elemental abundances of C, N, O, Al, Si, S, Cr, Mn, Fe, Ni, and Zn in a sample of 14 damped Lyα systems (galaxies) with H I column density N(H I) ≥ 1020 cm−2, using high-quality spectra quasars obtained with the 10 m Keck telescope. To ensure accuracy, only weak, unsaturated absorption lines are used to derive ion column densities and elemental abundances. Combining these abundance measurements with similar measurements in the literature, we investigate the chemical evolution of damped Lyα galaxies based on a sample of 23 systems in the redshift range 0.7 3 in our sample have (Fe/H) around 1/100 solar or less. In comparison, a large fraction of the damped Lyα galaxies at z < 3 have reached 10 times higher metallicity. This suggests that the time around z = 3 may be the epoch of galaxy formation in the sense that galaxies are beginning to form the bulk of their stars. Several other lines of evidence appear to point to the same conclusion, including the evolution of the neutral baryon content of damped Lyα galaxies, the evolution in the quasar space density, and the morphology of z < 3 galaxies. 4. The relative abundance patterns of the elements studied here clearly indicate that the bulk of heavy elements in these high-redshift galaxies were produced by Type II supernovae; there is little evidence for significant contributions from stellar mass loss of low- to intermediate-mass stars or from Type Ia supernovae. 5. Although earlier studies have attributed the overabundance of Zn relative to Cr or Fe found in damped Lyα galaxies to selective depletion of Cr and Fe by dust grains, such an interpretation is inconsistent with many of the other elemental abundance ratios seen in these galaxies, most notably N/O and Mn/Fe. Several other tests also indicate that thereis no significant evidence for dust depletion in these galaxies. We suggest that the overabundance of Zn relative to Cr in damped Lyα galaxies may be intrinsic to their stellar nucleosynthesis. If this interpretation is correct, it will provide important new information to the theory of stellar nucleosynthesis. 6. The absorption profiles of Al III in damped Lyα galaxies are found to resemble those of the low ionization lines. The profiles of Si IV and C IV absorption, while resembling each other in general, are almost always different from those of the low-ionization absorption lines. These results suggest that Al III is probably produced in the same physical region as the low-ionization species in the absorbing galaxies, while the high-ionization species (Si IV and C IV) mostly likely come from distinct physical regions. 7. We discuss possible ways to obtain information on the history of star formation (i.e., continuous or episodic) in damped Lyα galaxies and on the shapes of the stellar initial mass functions. 8. We review the evidence for, and against, the hypothesis that damped Lyα galaxies are disks or protodisks at high redshifts and discuss the implications. 9. We determine upper limits on the temperature of the cosmic microwave background radiation at several redshifts using absorption from the fine-structure level of the C II ion. These upper limits are consistent with the predicted increase of TCMBwith redshift.