Data from the Copernicus satellite's ultraviolet telescope were used to survey column densities of atomic and molecular hydrogen from a large sample of early-type stars; these data have bearing on an eventual understanding of diffuse and dense interstellar clouds. Column densities are derived by fitting damping profiles to the observed spectra, most of which exhibit strong damping lines in the lower rotational levels surveyed. Plots of dust column density, fractional abundance of molecular hydrogen, and the logarithm of fractional abundance versus total gas column density are given for many of the stars; stars with abnormally large or small hydrogen column densities, as well as some distant stars at high galactic latitudes, are considered. Equilibrium and nonequilibrium theories accounting for the abundance of interstellar hydrogen are compared, and support is found in the data for an account which balances hydrogen formation on interstellar grains with destruction through photodissociation. Overall averages for atomic and molecular hydrogen levels in the galactic plane are also calculated.