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I am beginning to learn group theory (specifically finite groups) and I’m wondering which textbooks can help me.

So any suggestions for introductory texts?

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    $\begingroup$ Rotman's is pretty good. $\endgroup$ – MathematicsStudent1122 Jan 7 '19 at 1:54
  • $\begingroup$ While I wrote an answer, this will probably be closed as either a duplicate or primarily opinion based, in fact I should probably vote to close myself: math.stackexchange.com/q/25506/90543 $\endgroup$ – jgon Jan 7 '19 at 2:14
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There are quite a few (very) good textbooks on finite groups out there. My favourite is Isaacs' "Finite Group Theory", but I wouldn't recommend it as a first textbook. Robinson's "A Course in the Theory of Groups" and Rose's "A Course on Group Theory" are both excellent.

In my opinion, though, the best book to read as a first when it comes to group theory is Smith's and Tabachnikova's "Topics in Group Theory".

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My introduction to groups (and algebra in general) was I.N. Herstein's Topics in Algebra. It begins with the theory of groups (covering what I would regard as the essential basics), but also covers rings, fields, vector spaces, and linear transformations. It's short, well written, and has a lot of good exercises.

I also really like Michael Artin's Algebra, which again is an introductory algebra textbook, but it includes quite a lot of good material on groups. I would say it's a bit more comprehensive than Herstein, and also very well written of course.

Lastly, I've gotten a lot of mileage out of Milne's course notes, which between them cover almost all of the algebra I've ever needed to know. It's been a while since I've read his group theory notes, but they're free on his website, so it's worth checking out.

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