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I am looking for some elementary books (may be introduction) about Spin structure in general, and Spin structure on Riemannian manifolds. Someone can help me? Thanks a lot!

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Here is a short paper of lecture notes. The first couple of pages introduce $Spin$ and $Spin^c$ structures on 4-manifolds. php.indiana.edu/~pkirk/papers/SW%20seminar%20notes.pdf –  Neal Mar 13 '13 at 17:55
    
You might find these notes helpful: empg.maths.ed.ac.uk/Activities/Spin/SpinNotes.pdf –  Henry T. Horton Mar 13 '13 at 17:59
    
Milnor has a classic paper in l'enseignement mathematique on this topic. –  Ryan Budney Mar 13 '13 at 18:39
    
Thanks every one! –  mapping Mar 13 '13 at 20:09

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