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A Comprehensive Introduction to Differential Geometry Michael Spivak
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Hang in there, spivak volume two is the best differential geometry book on the planet. For differential geometry, the book "Introduction to smooth manifolds" by Lee is good, but it presupposes (a little bit) of topology. Spivak, in A Comprehensive Introduction to Differential Geometry, I has an appendix on non-metrisable manifolds. Complete with chapter-by-chapter exercises, an overview of general relativity, and brief biographies of historical figures, this comprehensive textbook presents a valuable introduction to differential geometry. Comprehensive intro to diff geometry by Spivak Vol2. A Comprehensive Introduction to Differential Geometry, Volume I, 2nd edition, Wilmington, Delaware: Publish or Perish, 591. He starts (in the appendix) by defining a manifold to be a Hausdorff locally Euclidean space. In Differential Geometry is being discussed at Physics Forums. "This textbook, probably the best introduction to differential geometry to be published since Eisenhart's, greatly benefits from the author's knowledge of what to avoid, something that a beginner is likely to miss. It seems the course is being taught almost verbatim from this book despite the official textbook being the first volume of Spivak's A Comprehensive Introduction to Differential Geometry.