This book is based on lectures given at Harvard University during the academic year 1960-1961. The presentation assumes knowledge of the elements of modern algebra (groups, vector spaces, etc.) and point-set topology and some elementary analysis. Rather than giving all the basic information or touching upon every topic in the field, this work treats various selected topics in differential geometry. The author concisely addresses standard material and spreads exercises throughout the text. His reprint has two additions to the original volume: a paper written jointly with V. Guillemin at the beginning of a period of intense interest in the equivalence problem and a short description from the author on results in the field that occurred between the first and the second printings.
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This second edition of Sternberg's well-known book on advanced differential geometry contains two additional appendices, each with an extensive bibliography. It is self-contained, the first chapter being a treatment of multilinear algebra, concluding with some of the finer properties of exterior equations required by the method of moving frames and Cartan's theory of differential equations. This volume includes References and an Index.
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