We present a spectroscopic survey for moderate-redshift absorption features from damped Ly alpha and Lyman-limit absorption systems. The survey is based on a set of optimally extracted and co-added International Ultraviolet Explorer spectra of QSOs, BL Lac objects, and Seyfert galaxies. Results of this survey are combined with those of previous surveys carried out at optical wavelengths in order to examine evolution of the gaseous content of the universe over the redshift interval 0.008 less than or similar to z less than or similar to 3.5. The main results of the survey are that (1) the product of the absorption cross section and the comoving spatial number density of damped Ly alpha absorption systems does not appear to evolve strongly over the redshift interval 0.008 less than or similar to z less than or similar to 3.5, (2) the cosmological mass density Omega(g)(z) of neutral gas associated with damped Ly alpha absorption systems appears to decrease significantly from z approximate to 3.5 to approximate to 0.008, and (3) the observed evolution of Omega(g)(z) results from a steady decrease in the incidence of high column density absorption systems with decreasing redshift. Together these results suggest that the average mass of neutral gas per absorption system decreases with time, which is qualitatively cosistent wth the hypothesis that the observed evolution of Omega(g)(z) results from the consumption of gas into stars at z less than or similar to 3.5. We present additional arguments supporting this hypothesis and assess the implications of the observations of Omega(g)(z) for scenarios of galaxy formation and evolution. Under a ''closed box assumption'' we determine a characteristic epoch z(s) of star formation in galaxies of z(s) = 2-3 and a characteristic timescale tau(s) of star formation in galaxies of tau(s) = 0.5-1.0 x 10(9) h(-1) yr at z greater than or equal to 1.5. Considering recent chemical abundance measurements by Pettini et al. and others we conclude that the cosmic metallicity at z approximate to 2.5 is given by log Z(z approximate to 2.5)/Z(circle dot) = -1.0 +/- 0.5. Comparing the inferred cosmological mass density of metals in gas and stars at the epoch z(s) with the nominal cosmological mass density of metals in nearby galaxies, we conclude that the characteristic epoch of metal production in galaxies occurred after the characteristic epoch of star formation in galaxies. The implication of this result is that the bulk of stars in nearby galaxies should be metal poor, whereas only a small fraction of the disk stars in the solar neighborhood are actually metal poor. This inconsistency represents a ''cosmic G-dwarf problem'' in that a straightforward interpretation of our observations predicts many more metal-poor stars than are found in the solar neighborhood. We propose that the cosmic G-dwarf problem may be resolved if damped Ly alpha absorption systems trace not only galactic disk evolution, as suggested previously by Wolfe, but also galactic spheroid evolution.