We calculate the intergalactic photon density as a function of both energy and redshift for 0 < z < 6 for photon energies from.003 eV to the Lyman limit cutoff at 13.6 eV in a CDM universe with = 0.7 and sub(m) = 0.3. The basic features of our backward-evolution model for galaxies were developed in earlier papers by Malkan & Stecker. With a few improvements, we find that this evolutionary model gives predictions of new deep number counts from Spitzer, as well as a calculation of the spectral energy distribution of the diffuse infrared background, which are in good agreement with the data. We then use our calculated intergalactic photon densities to extend previous work on the absorption of high-energy g-rays in intergalactic space owing to interactions with low-energy photons and the 2.7 K cosmic microwave background radiation. We calculate the optical depth of the universe, t, for g-rays having energies from 4 GeV to 100 TeV emitted by sources at redshifts from 0 to 5. We also give an analytic fit with numerical coefficients for approximating t(Eg, z). As an example of the application of our results, we calculate the absorbed spectrum of the blazar PKS 2155-304 at z = 0.117 and compare it with the spectrum observed by the HESS air Cerenkov g-ray telescope array.