This is a translation from German of an article originally published inProceedings of the Mathematical-Natural Science Section of the Mainz Academy of Science and Literature, Nr. 11, 1961 (pp. 792 837) (printed by Franz Steiner and Co, Wiesbaden), which is Paper IV in the series “Exact Solutions of the Field Equations of General Relativity Theory” by Pascual Jordan, Jürgen Ehlers, Wolfgang Kundt and Rainer K. Sachs. The translation has been carried out by G. F. R. Ellis (Department of Applied Mathematics, University of Cape Town), assisted by P. K. S. Dunsby, so that this outstanding review paper can be readily accessible to workers in the field today. As far as possible, the translation has preserved both the spirit and the form of the original paper. Despite its age, it remains one of the best reviews available in this area.