Discrete Subgroups and Ergodic Theory**Editorial note. After consultation with G. A. Margulis it was agreed to make some changes directly on the original manuscript, without returning it to him, in order to save time. A. Borel kindly provided the necessary revision, including an additional argument supplied by G. Prasad in the proof of Lemma A. The appendix in the original manuscript has been transformed and reorganized into Section 4; the historical background material and the bibliography have been corrected and updated. The editors wish to thank A. Borel and G. Prasad for their help, still taking ultimate responsibility for making the changes.