Introductory Group theory textbook Which textbook is good for introductory group theory?
 A: If you mean an intro to abstract algebra, A book of abstract algebra by Charles C. Pinter is great. See the reviews on Amazon.
A: A very intuitive one is this: N. Carter, Visual Group Theory, MAA 2009.
A: I don't know any intro books dedicated solely to t group theory (im sure they exist), but I found Gallian's Contemporary Abstract Algebra to be incredibly useful as an intro book. The first section is dedicated to groups, and then theres equally good expositions on rings and fields. a little pricey, but really worth it in my opinion. Gallians website also has a ton of great supplementary material
A: My personal opinion is that "Artin, 2nd Ed." is much better than "Dummit & Foote" for an "introductory" text. I think it gives a more intuitive treatment of the material than "D&F." 
This can be coupled with Benedict Gross's free video lectures which follow "Artin."
http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra
(Although the lectures follow the first edition, the combination provides an outstanding learning experience. A real pleasure.)
A: Here are some good books:


*

*Algebra, Abstract and concrete by Fred Goodman,  it's available for download.

*Abstract Algebra by Dummit and Foote.

*A first course in Abstract Algebra by John. B Fraleigh.
A: What about the book An introduction to the Theory of Groups by Joseph Rotman?
It is in my opinion a classic.
A: 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.
A: 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.   
A: Antonio Machì, Groups: An Introduction to Ideas and Methods of the Theory of Groups.
A: You can try any undergraduate abstract algebra book like Topics in Algebra: I. N. Herstein, Algebra by Michael Artin, Abstract Algebra by Gallian,or  A First Course in Abstract Algebra by Rotman. Also, there's a book nice book solely dedicated to group theory by Armstrong, Groups and Symmetries.
A: I study group theory from abstract algebra by dummit and foote third ed , 
this text is great , it take you step by step and have many examples , exercises and its explanation is clear .. 
it's a great text .. 

added :
I tried to study from artin but i found it so bad - for me - it's a difficult and the explaination is not clear also it doesn't cover many things in the topic 
for instance, when it talks about isomorphisms theorems , it show the first theorem only but in dummit the 4 theorems is showed with clear explanation 
A: You could try A Book of Abstract Algebra, 2nd ed. by C.C. Pinter.
It is a wonderful Dover book and the first eleven chapters are group theory.
Peruse it on Amazon and see if it fits your needs.
You can also find out which book the class is using and peruse your library.
Enjoy!
A: I strongly recommend Frederick M. Goodman, Algebra: Abstract and Concrete
Also it is a free source and in my opinion the best introduction to groups and fields that a student could possibly have. Prerequisites are not much except some experience and patience to work through problems (there are many good problems in this text) and read and understand the many proofs. A theme in this book is to use simple symmetries and rotations to introduce the axiomatic concept of a group which in my opinion can be a little difficult to grasp with just it's definition alone. Group homomorphisms and isomorphism, measure of groups commutative through commutator group, cosets, quotient groups and isomorphism theorems, Lagrange' theorem about order of groups.The theories they introduce are then easy to grasp. Finally an introduction to product groups, then on to generalize many group theoretic structures to that of fields. Many examples are from linear algebra. I think this book would get a student well on there way to a healthy knowledge of group theory. After completion of this book I think you would feel ready to go on to study abstract algebras in general and on to the study of universal algebra. 
Unfortunately I can not provide a reference for these fields that can compare to the wonderful methods used in this book. 
A: Since it was not cited so far, I recommend J.S. Milne's Group Theory.
