The Byurakan/Hamburg/ROSAT Catalogue (BHRC) of the optical identifications of X-ray sources is presented. The BHRC includes all 2791 sources from the ROSAT-FSC with |b| ≥ 30• , δ ≥ 0 • and ROSAT count rate CR > 0.04 cts s −1 . For the optical identifications, we used 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 motions), the NVSS and FIRST radio, and the IRAS and 2MASS infrared catalogues. From the DSS images we obtained positional, brightness, color, extension, variability, proper motion information, and measured the optical-to-X-ray distance. Based on the DSS images, a morphological classification was made. Available SIMBAD and NED data were used as well. Cross-correlations were made with AGN, white dwarf, and cataclysmic variable catalogues (322/8/7 associations, respectively). We managed to identify 97% of sources (2696 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. We find that some of the latest 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 sources, and the bright galaxies and groups of galaxies comprise 9.2%. We found a number of close galaxy pairs (possibly interacting/merging galaxies) that are counterparts for X-ray sources (3.0%), as well as 1.0% WDs and 0.4% CVs. The BHRC may be used for selection and for studies of samples of various classes of X-ray emitters.