This first English-language edition is a completely revised and expanded version of Die Umlaufgetriebe, published by the Springer-Verlag in 1971. It will be extremely useful to American engineers since it stresses the efficiencies of new and existing transmission designs and provides concise guide rules as well as worksheets. A thorough understanding of the sometimes difficult material is facilitated through the use of both schematic and symbolic diagrams. The book is profusely illustrated and analyzes many applications. These drives receive an unusually clear treatment because at Dr. Müller's discovery of their perfect analogy to the simple epicyclic drive trains. Unified methods of analysis and synthesis of complex drives are employed throughout, suggesting that further simplifications may be possible through the use of a multivalued logic system which is analogous to the bivalent logic system of digital electronics. This book presents a clear and concise description of a multitude of revolving gear trains in terms common to all, whereas previous publications have been limited to treatment on interesting subproblems. Its well-reasoned definitions and classifications will aid engineers in the selection and design of the best drives for any given application.