The ROSAT Deep Survey in the Lockman Hole contains a complete sample of 50 X-ray sources with fluxes in the 0.5-2.0 keV band larger than 5.5E-15 erg/cm2/s. Previous work has provided optical identification of 46 of the 50 X-ray sources; over 75% of the sources are AGNs (Schmidt et al. 1998). We present now the atlas of optical finding charts and the full description of the spectra, including emission line properties of the optical counterparts, which are important for the object classification. New optical/infrared observations of three of the four unidentified sources show that one source is an AGN and two sources with an unusually large ratio of X-ray to optical flux have counterparts in the K-band suggesting that they are obscured AGNs. Furthermore, we found evidence from radio emission that the remaining unidentified source is a powerful radio galaxy (AGN). We thus obtain a 100% completeness. During the course of our optical identification work, we obtained optical spectr a of 83 field galaxies, of which 67 were narrow-emission line galaxies (NELG). We demonstrate that it is highly unlikely that a significant number of NELG are physically associated with X-ray sources.