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I want to learn about smooth manifolds, I have never studied them before, but I have a good background in Algebra. Can any one recomend some good introductory books?

Thanks

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Check out Introduction to Smooth Manifolds by John Lee, Differentiable Manifolds and Riemannian Geometry by William Boothby and Differentiable Manifolds by Lawrence Conlon.

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Lee's book seems very good. –  littleO Nov 6 '12 at 19:21
    
Thanks for the compliments. I just want to point out that the PDF that @amWhy linked to is a very early (and very buggy!) draft of the first edition of my Introduction to Smooth Manifolds, which somehow managed to escape into the wild and has now been posted on a number of sites in violation of copyright. Download it if you want, but caveat emptor. The published first edition is more reliable, and the second edition is much better. Just so you know. –  Jack Lee Nov 7 '12 at 1:11
    
@JackLee Thanks for your caveat! Good to know! I will, at once, delete my comment with the link - impressive as it was, even if buggy, as you say. I did not know that there was a violation of the copyright! –  amWhy Nov 7 '12 at 1:20
    
Here's a link to Lee's book, for anyone interested... –  amWhy Nov 7 '12 at 2:10
    
Springer link. Perhaps useful to someone –  leo Dec 14 '12 at 3:28

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