This table contains the Byurakan/Hamburg/ROSAT Catalog (BHRC) of the optical identifications of X-ray sources. The BHRC includes all 2791 X-ray sources from the ROSAT Faint Source Catalog (ROSAT-FSC, CDS Catalog <IX/29>) with galactic latitude |b| >= 30 degrees, declination >= 0 degrees, and ROSAT PSPC count rate CR > 0.04 ct/s. The optical identifications were carried out using the Hamburg Quasar Survey (HQS) digitized spectroscopic plates, the DSS1 and DSS2 (blue, red, and IR) images, the MAPS photometric data, the USNO-B1.0 (for proper motion), the NVSS and FIRST radio, and the IRAS and 2MASS infrared catalogs. From the DSS images, positional, brightness, color, extension, variability, and proper-motion information, the optical-to-X-ray positional offsets were obtained and a morphological classification was made. Available SIMBAD and NED data were also utilized. Cross-correlations were made with AGN, white dwarf, and cataclysmic variable catalogs (322, 8 and 7 associations, respectively). The authors managed to identify 97% of the sources (2696/2791 sources) that are associated with 3202 optical objects. 2248 X-ray sources have a single optical counterpart, 144 have a double or multiple optical counterpart (binaries, galaxy groups, etc.), and 304 have ambiguous identifications (some of the latter might actually be blends of two X-ray sources that were not resolved by ROSAT). The QSOs and AGN represent the largest group of X-ray counterparts (56.2%); bright stars (including late-type stars, but excluding WDs and CVs) are counterparts for 33.2% of the sources, and bright galaxies and groups of galaxies comprise 9.2%. A number of close galaxy pairs (possibly interacting/merging galaxies) are found as counterparts for X-ray sources (3.0%), as well as 1.0% WDs and 0.4% CVs. The BHRC may be used for the selection and study of samples of the various classes of X-ray emitters: the table gives all the available multiwavelength data for the identified sources. This table was created by the HEASARC in June 2006 based on CDS table J/A+A/449/425/table1.dat This is a service provided by NASA HEASARC .