TITLE: Choosing an advanced group theory text: concerns
QUESTION [27 upvotes]: In this question, An Introduction to the Theory of Groups by Rotman is recommended twice as a good second-course group theory text.  However, after reading the reviews here, and seeing this pdf of what seems to be corrections to Rotman, I am pretty concerned about the apparently many errors in the text.  While some errors and their corrections may be pretty self-evident, I would hate to constantly be worrying about developing some misconception as a result of some fact that isn't presented quite as it should be.

To those who have read An Introduction to the Theory of Groups by Rotman: do you feel the errors are a serious concern/disruption to the flow of the text, or is the book still pretty navigable?

Also recommended in the question linked to above was A Course in the Theory of Groups by Robinson.  I really like the look of this text, based on the table of contents and the group-theoretic concepts that really interest me.
The Robinson text is said (in the linked-to question) to 'move pretty quickly into deeper waters.'  My background consists of basic group theory, ring theory, field theory, a little Galois theory, linear algebra, topology, real analysis, and graph theory (I have seen a decent amount of material and have been self-studying for a few years now).  

Do you think that I can reasonably wade into these deeper waters without going in over my head and drowning?  I realize this is a little subjective since no one knows my exact abilities, but I love group theory and am definitely willing to put some real effort into it.

Thanks in advance for the advice.

REPLY [15 votes]: Books I love, approximately in the order I could understand them (ignoring publication dates; also you might notice groups are finite unless otherwise specified):


Rotman's Group Theory (actually I don't really like it anymore, but I loved it back in the day)
Hall's Theory of Groups (awesome, low key, some deep results)



Isaacs's Finite Group Theory
Alperin–Bell Groups and Representations (for GL and Sylow; short)
Wehrfritz's Second Course (for solvable ideas)
Suzuki's Group Theory (elementary, but covers some serious matrial)



Robinson's Theory of Groups (working up to infinite soluble groups and finiteness conditions)
Hans–Kurzweil Theory of Finite Groups (clean, crisp; was the best until Isaacs's; still has best description of the transfer homomorphism, but Isaacs gives a better description of transfer itelf)
Gorenstein's Finite Groups (classic; you can start it earlier, but the maturity level required is uneven; probably need Isaacs's CTFG first)
Aschbacher's Finite Group Theory (clean, crisp; if you understand a chapter, then its amazing, but some chapters you might not get, and there is not much there to help you)



Doerk–Hawkes Finite Soluble Groups (the first two background chapters are actually the first three volumes of Endliche Gruppe condensed)
Huppert's Endliche Gruppe
P. Hall's Collected Works (well, I only read the finite ones)


Also try to read Isaacs's Character Theory of Finite Groups as soon as you can. I suspect it should be fine after Rotman or Hall. After that, James–Liebeck's Representations and Characters of Groups continues the same path. You can get pretty far without character theory, but it's just silly not to bask in its awesomeness.
Wilson's Finite Simple Groups, Carter's Simple Groups of Lie Type, Holt–Plesken Perfect groups, Leedham-Greene–McKay Structure of Groups of Prime Power Order, and Malle–Testerman Linear Algebraic Groups and Finite Groups of Lie Type are amazing too, but you probably know if you need them.
At any rate, this should give you an idea of the wonderful things you can read. :-)