Algebra (Graduate Texts in Mathematics, 211)

It is not often that an author of a graduate textbook shares their understanding rather than merely provide a collection of theorems and proofs. Lang always delivers on this front. I'm partial to analysis myself, so I was certainly hesitant picking up this tome. But you'll find that it has everything you need (and much more). I primarily used the first four chapters, as well as the chapter on algebraic varieties. Each chapter is concise and written in a conversational style. There are many many great exercises as well.

Good graduate level text on abstract algebra. I paired this with sitting in on some lectures in a graduate level course on the subject (Groups and Rings specifically). A lot of proofs/exercises, you get a better feel for it through doing your own proofs and defining your own problems to solve.

I really like the book. It can be rough but every time I have sat down and really tried to figure out what Lang is doing in some proof, I come out having learned so much. Additionally, his style really emphasizes the main ideas (which is the most important thing in my mind). Also, there is a lot of supplementary material (eg. Bergman's "A Companion to Lang's Algebra", (just google it)) so it is relatively easy to fill in the details that you get really hung up on. These reasons have made the book my first choice to read up on something that I don't fully grasp. I also really enjoy the random examples he throws in from all over the place. It's pretty cool when you're sitting in class learning something new only to recognize it as that weird example from Lang that you didn't quite understand at the time.

I covet Lang's algebra for the problem sets. Other writers stoop to conquer, with the hand - holding and low - expectations. Lang expects you not just to understand him but to keep up with him, to not only follow but close the gap. This text is tough-love. His problem sets will terrify initially. They'll bog you down. But they'll help you get your sea legs. His questions, hints and problems are the only ones that consistently provoke me into navigating through an algebraic world of my own making. I would not trade that experience for all the compassion of most other texts. A true algebraist will tell you must get this book. It will remain relevant for a long time.

As most of the books written by Prof. Lang, this book is a great compilation, it has what it needs to have, nothing more, nothing less. If you are in Math or any related field, and need a book to refresh your knowledge on Abstract Algebra, this is your book. though, I took a course in Grad School from this book, and I don't recomend it. Fortunatelly I still had the books from my undegrad courses (Rotman's Group Theory book is great), and I did remember the old courses anyway, but I really discourage the usage of this book as a lecture book.

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A very useful book! Although It was hard to read at first, it became a good reference once I got used to the structure of the book.