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From many books on differential geometry, the one that caught my attention was Hick's book. It seems to be concise and self-contained, which are very good features if one is trying to self-teach the subject. This is my case: I want to learn some differential geometry, specially the notion of manifolds and its related concepts. I have a background on analysis but I wonder if this is the best book to start. To be sincere, the most attractive feature of the book is that it is a short book; for now, I want to learn the basics of the theory and taking a book with 300+ pages seems really exhausting and little focused. Are there alternative books or is it the ideal place to start?

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  • $\begingroup$ I always liked Hick's book. It's concise and has most of the essential topics. You'll want to read more later, but I think it's a good way to start. $\endgroup$ – Deane May 24 at 16:21
  • $\begingroup$ Hicks, not Hick! $\endgroup$ – Ted Shifrin May 25 at 4:21
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A good starter book is Spivak Vol 1 which starts on manifolds, or his Calculus on Manifolds. You don't have to read cover to cover, just glance through the table of contents and read those chapters you're interested in learning (especially when you have some analysis background), and maybe skim other sections just to get some ideas.

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