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"Advanced Undergraduate" my ass. This book is NOT for you until you've nosed around in Manifold Theory, Differential Geometry, Differential Forms and Topology for a good year or two. It provides fantastically concise summaries of some difficult subjects for people who already know but it is not an introductory text by any means. However, coming back to it with a little context later justifies it as a good reference, but Lee does a much better job of exposition in his 'Introduction to Smooth Manifolds'.