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I am interesting in learning about (topological) K-theory. As far as I can see there are 3 main references used:

1) Atiyah's book: This looks to be very readable and requires minimal pre-requesities. However, the big downside is there are no exercises

2) Allan Hatcher's online notes: If his Algebraic Topology book is any guide, this should be an excellent readable account of K-theory. I note that this is unfinished however.

3) Karoubi's Book: A nice looking book - perhaps less readable than Atiyah? (personal opinion, based on a quick scan)

Are there any other references/on-line notes available? I am probably leaning towards an Atiyah/Hatcher combination.

(Can this be made community-wiki?)

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There's also Segal's paper "Equivariant K-Theory" if you want your K-Theory to have a $G$ action. He runs through some of the basics. –  Joe Johnson 126 Apr 22 '11 at 10:41
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swoosh- wham. Yes it can. (Wiki-hammered) –  Willie Wong Apr 22 '11 at 13:40

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up vote 6 down vote accepted

"Complex Topological K-Theory" by Efton Park is a pretty decent introduction to topological K-Theory, but I'd actually go with Karoubi's book.

There is also a chapter on K-Theory in John Peter May's "A Concise Course in Algebraic Topology", which is in my opinion the best text on algebraic topology currently available, including some references and recommended further reading.

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That chapter of May is really cool! –  BBischof Apr 22 '11 at 14:03
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All of May is really cool :D –  Alexander Thumm Apr 22 '11 at 17:32
    
Good point! I like that book a lot. –  BBischof Apr 22 '11 at 21:36
    
Thanks for the references. I'd love to be able to digest all of May's book, but it is very heavy for a first read! I'll have a look further at Karoubi –  Juan S Apr 23 '11 at 0:51
    
@Qwirk: It is indeed very heavy, but also very rewarding. A good strategy would be to take May's book as a guideline and complement with easier literature once you feel stuck or unable to fill in the details. –  Alexander Thumm Apr 23 '11 at 11:02

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