We present an extensive spectroscopic study of 10 rich, southern, X-ray clusters of galaxies. Between 40 and 200 redshifts have been obtained in the field of each of the clusters, which cover a wide range of morphological types and richnesses. Applying rigorous statistical analyses to the total data base of 1000 precise radial velocities provides the necessary information to undertake a thorough dynamical investigation of these individual clusters and of cluster systems in general. Further papers will present the photometry, X-ray data, dynamical models, and X-ray gas models for the clusters. Such an analysis will yield the distribution of luminous and dark matter, the importance of substructure, and details of the dynamics in the clusters, along with an illustration of environmental and evolutionary effects in clusters of galaxies.