Future quasar absorption line studies will combine insights gained from detailed analyses of individual systems with conclusions drawn from the large statistical samples assembled over cosmic time. Evolution of the ensemble of absorption profiles generated by the universal collective of intervening structures is a result of the combined effects of numerous processes. These include growth of structure, star formation, morphological evolution of galaxies, galaxy mergers, and changes in the extragalactic background radiation. Here, we summarize the best present statistical data and likely interpretations for the different classes of absorbers. The number of lines per unit redshift for various populations of absorbers is represented by a power law dN/dz (1 + z). For a universe with only the cosmological evolution due to expansion, = 1.0 for deceleration parameter q0 = 0 and = 0.5 for q0 = 0.5.