Written to fill the need for establishing a point of reference in the copious but scattered literature of the field. The Catalogue of Radial Velocities of Galaxies is a comprehensive survey of radical velocities or redshifts of the galaxies in the universe. It lists all available measurements for each Galaxy including Russian citations from the measurement of the first radial velocity by Slipher in 1914 through December 1980. In a unique feature it includes optical and radio measurements for all galaxies in both the northern and southern hemispheres. In bringing together uniformly and concisely all published references, the Catalogue affords readers the opportunity to evaluate the data and determine which measurement or measurements represent a ’good’ measurement for the radial velocity of each Galaxy. In preparing the Catalogue the authors not only compiled the available data, but checked identifications, re measured precise coordinates, and noted discordant redshift values. In addition to including more galaxies than any other existing redshift catalogue, the work reflects the most thorough research and careful evaluation. Indeed the availability in a single scrupulously documented source of all original measurements will save researchers incalculable time and effort. The catalogue sites 967 references from which radial velocities of 8250 galaxies have been obtained. Since many galaxies were measured more than once, the total number of radio velocities listed is 13,672. The galaxies are ordered by increasing right ascension, with particular attention paid to providing accurate positions and names. Radio galaxies and Seyfert galaxies are identified. Lists of all Messier Galaxies (39), Arp peculiar objects (221), Vorontsov/Velyaminov interacting galaxies (230) and Markarian galaxies (773), whose radial velocities appear in the Catalogue are also given in the appendices.