Introductory Group theory textbook [closed]

What about the book An introduction to the Theory of Groups by Joseph Rotman?
It is in my opinion a classic.

I think the group theory part (= first 6 chapters) of Abstract Algebra by Dummit and Foote is quite good. Personally, I dislike Armstrong's book Groups and Symmetry; his style is too informal to my taste, and definitions are hidden in the text.

A concise, clear one is Humprhey's A Course in Group Theory, it gets you quickly to the core of the subject.

For a 'second' course I like the Universitext The Theory of Finite Groups: An Introduction by Kurzweil and Stellmacher.

In addition to the Rotman and Kurtzwell books suggested below (above?), I'll make some other suggestions.

One of the best introductions I've ever seen to basic group theory is in chapter 1 of I.Herstein's classic Topics In Algebra,2nd edition. This was my introduction to abstract algebra in an honors algebra course and I still think it's one of the truly great all-time algebra books. (I tell graduate students all the time who are worried about their qualifying exams in algebra-take out a copy of Herstein and see how many of his exercises you can do. If you can do most of them without getting stuck, you're ready for your qualifiers.)

A great cheap book in Dover paperback for graduate students is John Rose's A Course In Group Theory. This was one of the first books to extensively couch group theory in the language of group actions and it's still one of the best to do that. It covers everything in group theory that doesn't require representation theory.

Lastly, a book I had the pleasure of reading and reviewing for the MAA online is I. Martin Issacs' Finite Group Theory. This beautiful, comprehensive text is by a master of the subject and one of the best textbook authors active today. This book differs from the more classical texts in that it's more advanced than most of the others-it begins with the Sylow theorems and assumes basic group theory. As a result, it covers more sophisticated and recent topics than usually found in such texts, such as we meet several results that I doubt have ever appeared in book form before, such as the Chermak-Delgado measure. It's also masterfully written as all Issacs' texts are. It's definitely worth checking out if you're interested in group theory, especially for the very best students.

If you mean an intro to abstract algebra, A book of abstract algebra by Charles C. Pinter is great. See the reviews on Amazon.