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I'm searching for a freely available text that introduces topological and smooth manifolds. I don't need much, just their basic properties and a bit more motivation than the wikipedia articles offers. Maybe course notes of some course that covered them.

(Background: I skipped the classes where topolical manifolds were introduced, and now I can't solve any problem where they appear, and I would like to change this before the exam ;)

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up vote 1 down vote accepted

I am very sure these links will be very useful.

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@Benno. For good book, I will recommend Geometry of Differential Forms (Translations of Mathematical Monographs) by Shigeyuki Morita. – smanoos Jan 5 '12 at 22:59
Thanks, I'll look for it in our library. – Benno Jan 6 '12 at 12:26

Lee's books are great. There is also a very nice book by Tu called An Introduction to Manifolds which is relatively new.

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These books are not "freely available". – epimorphic Jun 1 '15 at 21:41

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