The IRS is an all-sky catalog of positions and proper motions that is based on the AGK3R (Corbin 1977, 1978) in the Northern Hemisphere and on the newly completed SRS (Smith et al. 1990) in the south. The data for the 36027 stars of the IRS were compiled in B1950.0 FK4 and then transformed to J2000.0 FK5. The IRS was compiled by matching 122 meridian circle catalogs with the AGK3R and SRS to provide the data base. Catalogs whose stars had been observed using screens to minimize the magnitude equation and that contained FK4 (Fricke and Kopff 1963) stars were used to form a preliminary system. These catalogs were reduced to the FK4 by direct comparison; the resulting positions and proper motions were then used to reduce all of the other catalogs. Thus, the IRS is a differential catalog compiled from 164,917 positions reduced to the FK4 system. The IRS is divided into two parts. Part 1 contains the stars having better observational histories and, therefore, more reliable positions and proper motions. This part constitutes 81 percent of the catalog; mean errors of the proper motions are 0.43 and 0.44 seconds of arc/century (4.3 and 4.4 mas/yr) in right ascension and declination, respectively. The stars in Part 2 have poor observational histories and consist mostly of objects for which only two catalog positions in one or both coordinates were available when the proper motions were computed. Where accuracy is the primary consideration, it is best to use only the stars in Part 1, while if the highest possible density is desired, the two parts should be combined, as they are systematically the same. The data included are catalog part, IRS number, equatorial coordinates (equinox, equator, epoch B1950.0 and J2000.0), centennial proper motions (B1950.0 and J2000.0), original epochs, weights for right ascension and declination, and reference data such as DM numbers (BD, CD, CPD), AGK3 and CPC2 designations, and an IAU-recommended IRS identifier (based on coordinates).