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I would like to know if there are any general references that you would suggest to learn about quantum groups? I have looked at some of the "standard" books, but I am wondering if someone is particularly fond of a certain reference and why.

Also, I am very interested in ms/phd thesis (particularly ms thesis) that deal with quantum groups(I find that ms thesis sometimes aim to prove a few major theorems about a subject and fill in the details, instead of setting out to discover new mathematics). Thanks in advance.

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I have converted the question to community wiki, as it's asking for a big list of references, and there is no single right answer. –  Zev Chonoles Jul 23 '11 at 16:32
Christian Kassel's "Quantum Groups" is an excellent book. –  Grumpy Parsnip Jul 23 '11 at 16:35
Are you more interested in the approach that builds the general theory or rather some nice applications (there are tons in physics alone) with theory mentioned along the way? –  Marek Jul 23 '11 at 16:37
@Marek, I am not interested in the application as much as the general theory. –  Edison Jul 23 '11 at 16:39
@Marek, can you suggest some literature(for a non-physicist) that treats the physics first and the math along the way? Thanks. –  Edison Jul 25 '11 at 17:24

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Our (Carter, Flath, Saito) "Classical and Quantum $6j$-Symbols," PUP does not cover the subject in general, but tells a lot of what is needed in the $U_q(sl_2)$ case.

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Brain dump: Kassel is good. Jantzen (Lectures on Quantum Groups) is nicely written and clear, it's my favourite. Majid (Foundations of Quantum Group Theory) is an option, I haven't read it. Lusztig's book has a reputation of being tough to read. Chari and Pressley (A Guide To...) is comprehensive and has some interesting material on knots, 3-manifolds, the KZ equation and the absolute Galois group.

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For starters you can check references in this question of mine on applications of Hopf algebras.

Here's an article or two that build a little theory of ${\mathfrak sl}_2$ related stuff. There are many similar articles on spin-chains where ${\mathfrak sl}_2$ deformations are naturally present.

References in the classic Di Francesco, Mathieu, Sénéchal on conformal field theory.

Another connection (via Yang-Baxter equation) is with integrable systems.

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