The Brera Multi-scale Wavelet ROSAT High Resolution Imager Source Catalog (BMW-HRI) is derived from all ROSAT HRI pointed observations with exposure time longer than 100 seconds available in the ROSAT public archives. The data were analyzed automatically using a wavelet detection algorithm suited to the detection and characterization of both point-like and extended sources. This algorithm is able to detect and disentangle sources in very crowded fields and/or in presence of extended or bright sources. Images have been also visually inspected after the analysis to ensure verification. The final catalog, derived from 4,303 observations, consists of 29,089 sources detected with a detection probability of greater or equal 4.2 sigma. For each source, the primary catalog entries provide name, position, count rate, flux and extension along with the relative errors. In addition, results of cross-correlations with existing catalogs at different wavelengths (FIRST, IRAS, 2MASS, and GSC2) are also reported. As an external check, the authors compared their catalog with the previously available ROSHRICAT catalog (both in its short and long versions) and were able to recover, for the short version, ~90% of the entries. The sky coverage of the entire HRI data set was computed by means of simulations. The complete BMW-HRI catalog provides a sky coverage of 732 square degrees down to a limiting flux of ~1x10^-12 erg/s/cm² and of 10 square degrees down to ~1x10^-14 erg/s/cm². The authors were able to compute the cosmological log(N)-log(S) distribution down to a flux of about 1.2x10^-14 erg/s/cm². This catalog was ingested by the HEASARC in March 2003, based upon the <a href="https://cdsarc.cds.unistra.fr/ftp/cats/IX/34">CDS Catalog IX/34</a> file catalog.dat.gz. This is a service provided by NASA HEASARC .