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I am going to start learning Abstract Algebra soon. I was originally going to start with Dummit and Foote, but I am starting to abandon that idea. I want to use a "hardcore" algebra book. I don't mind how terse a book is (I actually quite enjoy this), I can work my way around that so it isn't an issue. I just want a book that is used by the hardest grad schools, essentially the highest level algebra book there is, also one that covers perhaps the most material. To my understanding, Lang's graduate Algebra seems to fit this description, but I was wondering if you all could either recommend what you believe to be better, or confirm what I have heard. Thanks in advance for any response.

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    $\begingroup$ I don't think you'll be harmed going with D&F. Lang certainly fits the hardcore description and the exercises are really good, but I don't think most students can just sit down and work through it linearly. $\endgroup$ – Hoot Jul 4 '15 at 0:50
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    $\begingroup$ Yeah, it sounds like you want Lang. $\endgroup$ – Braindead Jul 4 '15 at 0:52
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    $\begingroup$ Nathan Jacobson's books "Basic Algebra I, II". $\endgroup$ – Matematleta Jul 4 '15 at 1:41
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Hungerford is great. You should prove the things he puts out as exercises. It will give you a strong grasp of Algebra. I used it to pass the Ph. D. qualifier at the University of Texas.

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  • $\begingroup$ Whereas at Rutgers it was the textbook for the algebra course I took. $\endgroup$ – Matt Samuel Jul 4 '15 at 2:28
  • $\begingroup$ Is Hungerford better than Lang? Does Hungerford cover more? Thanks for you reply by the way. $\endgroup$ – Sprinkle Jul 4 '15 at 2:30
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    $\begingroup$ I found it more readable than Lang. $\endgroup$ – ncmathsadist Jul 5 '15 at 20:14
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I liked P.M. Cohn's book, it came in 2 volumes and was easier to read. Jacobson is exhaustive, including specialized topics as constructing irreducible representations of $S_n$, but I always used Jacobson to read a specific topic something like 4 or 5 pages at a time.

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