Rating: 
Summary: I never knew math was this much fun!!!!
Review: Among all the branches of mathematics that I have come across in my undergraduate career I would have to say that Abstract Algebra was the best. Gallian's book made me appreciate the beauty and power of algebra. This book is full of surprises. It covers groups, rings and fields, and Gallian takes us into the lives of the mathematicians who have made this field of mathematics so ripe. There are ample references which I found helpful, and the book also has many real-world applications of Abstract Algebra, for instance RSA. The prose and the proofs are lucid and very precise. Each page of this book is worth reading! The price might be a little steep but it is worth it!
Rating:
Summary: I never knew math was this much fun!!!!
Review: Among all the branches of mathematics that I have come across in my undergraduate career I would have to say that Abstract Algebra was the best. Gallian's book made me appreciate the beauty and power of algebra. This book is full of surprises. It covers groups, rings and fields, and Gallian takes us into the lives of the mathematicians who have made this field of mathematics so ripe. There are ample references which I found helpful, and the book also has many real-world applications of Abstract Algebra, for instance RSA. The prose and the proofs are lucid and very precise. Each page of this book is worth reading! The price might be a little steep but it is worth it!
Rating: 
Summary: Relaxed introduction to abstract algebra
Review: An easy, relaxed introduction to groups and rings. There are lots of problems (most fairly easy, but some were difficult) to hone your skills. The biographical info at the end of each chapter made the book fun to read. It's not, however, a very rigorous book, and I personally didn't like all the info about cryptography. I completely disagree with the previous reviewer on one point- it's no good for a mathematical physics class. I don't think it even talks about continuous groups or Lie algebras, and if it does, it talks about them very briefly.
Rating:
Summary: An Excellent First Course!
Review: Gallian's algebra book is an excellent first course. It provides an inviting and clear introduction to abstract mathematics. Though not a rigorous, encyclopedic work like my own, it offers a fresh, friendly, and approachable style that will appeal to students from a wide variety of backgrounds. And if you aren't captured by the mathematics, the many Beatles references and other well placed quotes will still make this book a delight to read.
Rating:
Summary: An Excellent First Course!
Review: Gallian's algebra book is an excellent first course. It provides an inviting and clear introduction to abstract mathematics. Though not a rigorous, encyclopedic work like my own, it offers a fresh, friendly, and approachable style that will appeal to students from a wide variety of backgrounds. And if you aren't captured by the mathematics, the many Beatles references and other well placed quotes will still make this book a delight to read.
Rating:
Summary: Much better than Herstein, not as advanced as D&F
Review: I "grew up" on Gallian, which I think is a pretty good text. I think this text is more complete than Herstein, and if the students are not advanced enough for Dummit and Foote, this is the text to pick.For those advanced mathematicians out there, I highly recommend considering Dummit and Foote's text. It is very advanced, but also very readable.
Rating:
Summary: Much better than Herstein, not as advanced as D&F
Review: I "grew up" on Gallian, which I think is a pretty good text. I think this text is more complete than Herstein, and if the students are not advanced enough for Dummit and Foote, this is the text to pick. For those advanced mathematicians out there, I highly recommend considering Dummit and Foote's text. It is very advanced, but also very readable.
Rating: 
Summary: Gallian's poor algebra book.
Review: I agree with the other reviewers in the sense that it is ture Gallian's book is soft on theory and rigor, but oppositely I find this lack of real substance to be Gallian's deepest flaw. I give Gallian one star, basically for effort. I divide my critique into the following subcategories: Organization: Gallian's book is organized well enough in the sense that he opens each chapter with some commentary about the problems to be studied, or motivation, and then proceeds to go example, theorem, proof, example, example, example, example,..., example. This doesn't work, I think, because he spends too little time actually showing theorems and proofs, and sometimes he'll build an entire chapter on just two or three theorems, and fill the rest with useless commentary (which I'll mention again below). Readability: As for readability, for people who read math books at all (i.e., those who study outside of class), this book should be a nightmare. If you were to strip away all of the useless commentary/endless biographical insets/weblinks you would be left with probably about 30 pages of theorems and cumbersome proofs (by cumbersome, I don't mean involved, I mean unrefined). Gallian has failed to make a readable text because he presumes to have the omnipotence and foresight required for putting a full understanding of algebra and algebra history into one book. As a result, the excess commentary he makes and useless statements (for example, "In high school, students study polynomials with integrer, rational, real, and sometimes complex coefficients") distract a reader from the main points, and I rarely found myself rubbing my chin thinking how insightful something he said was. All in all, I feel as though the reading felt "hoakie" at best--like he was elbowing me in the side, winking, trying to get me to lie and say I thought what he was saying was insightful. Exercises: The exercises are often clumsily put together and the quotes before each problem set can get extremely patronizing. I remember thinking how cocky this Gallian fellow must be to presume that people can't do "his" problems. A joke, to say the least. In any case, they seem fine for all purposes -- if you're going into chemistry or an applied science that uses group theory. It's very obvious that our author believes that group theory is the pinnacle of the algebra experience and struggles to present topics from rings and fields. IF you are someone who likes group theory, fine. BUT Artin's book does everything Gallian does and more with group theory and builds the same ideas on more solid footing, using linear algebra excessively throuhout the book. For example, if you think I'm joking about Gallian's weakness, just look at the chapters on isometries and compare them to the chapters in Artin, and you'll see what I'm talking about. Peter Rabbit: Well, I do have at least one nice thing to say. As anyone can see, Gallian has a lot of examples, but this seems to be the only redeeming quality of the book. But that alone doesn't make an algebra book. Broad Commentary: If it's a softer touch you're looking for, I'd say go with Durbin -- he's easy to follow and an excellent writer. If it's group theory, examples, and a lot of wonderful exercises you want, go with Artin. Neither of those books get caught up in useless commentary. I've heard good and bad things about Fraleigh (sp?), but have no direct experience with that book. I would suggest, for those who don't want a hardcore book such as Herstein's Topics in Algebra, or M. Artin's Algebra, you should see Durbin's book. Durbin is also a softer book; it has many nice examples and is very well written. IF you are unavoidably made to use this book for a course, and if you want to learn to be more insightful/challange yourself to think/want to study, then I suggest you use any of Artin, Herstein, or Durbin as a companion (in that order, but I only place Artin above Herstein because Artin has more material in it, Herstein is a much better writer so you might choose him depending on which book you'll spend more time with).
Rating:
Summary: Real joy to read!
Review: I had to learn group theory in a hurry for my research, and a friend recommended this book to me. Abstract algebra can very quickly become boring, but Gallian's writing makes it all fun. Gallian is clearly very passionate about the subject, and covers the basics of abstract algebra very well. The presentation in this book is fairly verbose, and therefore does not cover very much of the more advanced topics in abstract algebra. Nonetheless, after reading this book I feel sufficiently confident and enlightened to continue my journey into abstract algebra. This book is highly recommended for beginners interested in starting learning abstract algebra.
Rating:
Summary: An excellent text on algebra!! Two thumbs up!
Review: I recently took an abstract algebra course that used this text. I come from a physics background and found that this book explains the mathematics, notations, and general concepts very well. I would like to add that I had the privilege to take an undergraduate course in Calculus from Dr. Gallian. His lectures were the best I have yet to experience. His enthusiasm is portrayed in his books just as in his classroom. If you want to learn the mathematics, then read Gallian's book.
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