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I recently finished a course in representation theory, and while I learned a lot from it, I know that there's a lot more in the subject that I missed. For the course we used Fulton and Harris as a reference, but really only took exercises from it; the course notes were the professor's own notes. And having read through Fulton and Harris a little, I realize that it's pretty hard to learn from.

So I'm looking for a text on representation theory geared toward early graduate students (or even advanced undergraduates) that have NO experience in the subject whatsoever. Preferably with lots of examples, computations, and loads of exercises that is generally considered good for self-study. I want to start at the beginning again and really develop my intuition and fill in gaps in my knowledge. My preference also is to work with finite groups, but I assume most books at the level I want cover finite groups at least some, and this is certainly not a deal-breaker. Anyone have any suggestions?

Perhaps that list narrows things too much, but anything that has a sufficient number of these qualities should do. Thank you!

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I can recommend this script, a beginner's course in representation theory is currently being taught at my university using it, and from what I have seen so far, it's quite well-written. – Jesko Hüttenhain Dec 20 '12 at 20:08
Thanks, I'll take a look at it! – Bey Dec 21 '12 at 6:16
up vote 3 down vote accepted

I really like Huppert's Character Theory of Finite Groups. Isaacs book under the same name is also very good, and probably easier to come by; it is about $10 on amazon. I read both of these as an undergraduate (and I hated Fulton and Harris).

There are a few differences between the two. Huppert was written after Isaacs and contains many more results about character degrees, especially where they tie into Huppert's $\sigma$-$\rho$ conjecture. Another thing I like about Huppert (and this is just a personal preference) is that it has slight module-theoretic bias, whereas Isaacs is entirely characters. Huppert also contains more elaborate examples. On the other hand, Isaacs covers projective representations in greater detail, and contains sections on Schur multipliers and Brauer theory, both of which are completely absent in Huppert. Both books have fantastic exposition.

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Thank you, I appreciate it! Amazon is selling Huppert's text for $266... any advice on finding it somewhere for less? – Bey Dec 21 '12 at 6:17
@Bey Try your university library. I just keep renting it out from mine over and over. :) – Alexander Gruber Dec 21 '12 at 6:44
Oh also I think I saw it for ~60 dollars on alibris or some used book site like that, but I don't remember which. – Alexander Gruber Dec 21 '12 at 6:44

Fourier Analysis on Finite Groups and Applications by Audrey Terras does not fit your specifications entirely, but is interestinng and has many applications.

Another book you could look at is Persi Diaconis.

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I've only briefly skimmed the beginning, but this book came to me highly recommended. Plus, it's free!

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