A Comprehensive Introduction to Differential Geometry, Volume 1 (3rd Edition)

Great book for amatures If you want a book that is rich with examples then this is it. The proofs are, for the most part, clear and concise, thus a person who is learning the material without the aid of an instructor can follow the logic. However, the author could have spent some more time developing topological ideas (thought he does have an appendix section that does a fair job of it) within the flow of the first chapter. I personally find appendices to be too distracting and tend to slow down the flow of the material in a particular chapter. Other than that, this is a great book if you want to learn differential geometry and the theory of smooth manifolds.