We have obtained echelle spectra of the nucleus of Markarian 231 in 1991 and 1994 and modeled the profiles of the sodium absorption lines that are blueshifted up to 7800 km s-1 less than the systemic recession velocity of this active galactic nucleus (AGN). We find that the broadest absorption line (system I) can best be fitted with a blend of multiple, optically thin components rather than a single, or a blend of many, saturated lines. The total column density of neutral sodium in this broad line is NNa I ≃1014 cm-2, a factor of 10 less than previous estimates. The line profile fit of the narrow Na I D absorption lines (systems II and III) yields a column density of NNa I 1012 cm-2 The variability of the absorption lines of Mrk 231 is seen again in the disappearance of an Na I D absorption line at 6015 Å sometime between 1991 and 1994 and a change in the profile of the broad absorption line. The weak absorption lines away from the broad system have similar column densities and Doppler velocity widths to those seen in absorption lines due to extended gas from galaxies illuminated by background QSOs. We find no evidence in the spectra of regions 5" east and west of the nucleus for Na I D absorption or the blend of Hα + [N II] emission at the velocity of system I that had been previously observed.We consider the He I absorption seen in optical spectra and in the Hubble Space Telescope (HST) Faint Object Spectrograph (FOS) spectrum of Smith et al., and we conclude that He I absorption arises from the metastable 23S level in statistical equilibrium due to irradiation by a dilute, steep spectrum radiation field; a similar mechanism to that proposed for Na I D and He I absorption seen in shell stars.