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Having studied some group theory in my last term at university, I've found it to be quite interesting, although it's also something I want to improve on (mainly when it comes to proving statements), so I figured that it might be worth doing some group theory slightly beyond what I need for this year, just to get a better feel for the topic in general.

However, when I've had a look around, the only good group theory books I've found seem to be those in the "Graduate Texts in Mathematics" series (for example Robinson's "A Course in the Theory of Groups") and therefore probably slightly too advanced for a first year. So, would anyone please be able to suggest a good book for self-studying first/second year group theory?

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Did you study some group theory in a class on abstract algebra? Or was the class exclusively on "Group Theory"? Whatever the case, what was the text you used? –  amWhy Jan 10 '13 at 16:51
The class was exclusively on Group Theory - however I didn't use any of the recommended textbooks as they were mainly for the old groups course (which was a mix of vectors, matrices and group theory) and I found that often they mixed the order of these chapters, therefore making it hard to actually just study the groups bit. However, I can tell you what topics we covered: Symmetric and dihedral groups, Cosets and Lagrange's theorem, Normal groups, quotient groups and isomorphisms (up to the first isomorphism theorem), direct products, group actions, and then matrix and Mobius groups. –  Andrew D Jan 10 '13 at 17:18
I want to recommend "Finite group theory" by Martin Isaacs. –  Myself Jan 10 '13 at 18:30
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2 Answers

up vote 5 down vote accepted

EDIT: from your response below your answer: I'd definitely check out Rotman's text. That's the text I'd recommend most highly.

Original post:

Look into Joseph Rotman's An Introduction to the Theory of Groups: that would be a good continuation from your initial semester studying group theory. (You can preview the book at the given link.)

(EDIT: what follows seems no longer to be relevant, as noted at the start of my answer, but may be a quick read/review, nonetheless.)

(in original post) If previewing the text looks too advanced, check out the Dover (hence inexpensive!) book by John Rose: A Course on Group Theory. That should bridge the gaps from initial exposure to group theory, and a more advanced text in group theory. (You can "preview" the book at the given link.)

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Ah okay then, thanks! I've found a .pdf of it online, but the quality isn't very good, so I'll just get a copy out of the library when I get back to university (or if I'm lucky find it in a bookshop somewhere). –  Andrew D Jan 10 '13 at 17:33
Try interlibrary loan, if your library doesn't have it? –  amWhy Jan 11 '13 at 0:40
I can just ask the library to buy it if they don't have it, and most likely they'd do so, so that isn't much of a problem - but if I particually liked it then I'd rather have a hard copy to keep. –  Andrew D Jan 11 '13 at 13:25
@AndrewD I'm the same way - I have acquired my own huge library for the same reason you mention. My one "weakness" in terms of "spending" is buying my own books! –  amWhy Jan 11 '13 at 13:28
I took a look at the amazon link you provided. There is a user who complained that two issues about Rotman's book, notation and typos. 25 of 25 viewers agree. I am okay with notation. I just have to get used to it. Typo is something I hate. I had terrible experience with a semigroup theory book. I struggled with one typo for an entire week. I am old and retired. No time to waste on this kind of thing anymore. I cannot find errata on internet. Do you know if errata exists? I want to make sure errata is available before I buy it. Thanks. –  scaaahu Jun 12 '13 at 6:15
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See the classical Joseph Rotman An Introduction to the Theory of Groups.

See too Introduction to Group Theory by Oleg Vladimirovič Bogopolʹskij.

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Rotman's text is fantastic. I second this recommendation. I used it to study for my first year qualifying exams. He starts off pretty slow and discusses permutation groups before ever defining an abstract group (which is a logical choice since these were, historically, some of the first groups studied). Robinson's text (the Springer GTM) is also nice, but moves pretty quickly into deeper waters. –  John Myers Jan 10 '13 at 17:09
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