The catalog gives redshifts for 329 Abell clusters, all those known to the authors in published or preprint form at the time of the compilation (through 1982). The data table has been compiled critically, based partially on a number of photometric distance estimators derived from the redshift data. These were used to evaluate probable accuracies of the redshifts and to resolve discrepancies among different values for the same clusters. The catalog includes Abell (1958) cluster numbers, redshifts, and the number of redshifts of different galaxies averaged to determine the cluster value. The machine version was prepared at the Astronomical Data Center, NASA/GSFC. Note that Struble and Rood published further compilations in 1987 (1987ApJS...63..543S) and 1991 (1991ApJS...77..363S). Other redshift compilations are also available in electronic form (see "See also" section below).