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I'm planning to take a phd-level Algebra class this fall semester and so I want to spend some of the summer going through a good first book. The phd course will assume knowledge of undergrad Algebra.

Is there something like a "baby Rudin" / gold-standard book for Algebra?

Is there also an easier book with both lots of exercises and solutions?

Thanks,

User001
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    Dummit and Foote? Hungerford is not too bad either but focuses way too much on the category theory aspects.. which are a bit pointless for what he does in my opinion. – Cameron Williams May 09 '16 at 03:38
  • Oo -- is this classical and rigorous or easy and full of exercises (like a schaum's outline book)? Thanks @cameronwilliams – User001 May 09 '16 at 03:40
  • seems like many people agree with you -- I will look it up now @cameronwilliams :) – User001 May 09 '16 at 03:41
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    I edited my comment. I forgot to hit enter. – Cameron Williams May 09 '16 at 03:42
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    Rigorous. Nothing like Schaum's.@User001 – R_D May 09 '16 at 03:42
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    If you want a text with a lot of exercises that are easy, go for Gilbert and Gilbert I guess? That text feels like a first year text though. – Cameron Williams May 09 '16 at 03:43
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    I also agree that Dummit and Foote is a very good book. However, my favorite is "Algebra:Chapter 0" by Aluffi. It is more catogery-oriented (which is great if you want to study algebra or topology/geometry) and goes further than D&F. And it has lots of exercises of various difficulties. – Nitrogen May 09 '16 at 03:44
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    @User001: This question has been asked many times on the site, for example: http://math.stackexchange.com/questions/54839/good-abstract-algebra-books-for-self-study?rq=1, http://math.stackexchange.com/questions/174596/good-problem-book-on-abstract-algebra?rq=1, http://math.stackexchange.com/questions/1413777/good-algebra-book-to-cover-these-topics?rq=1 – Moo May 09 '16 at 03:44
  • Ok got it - thanks, @rise :) – User001 May 09 '16 at 03:45
  • Before you study abstract algebra, you should study elementary number theory for a semester or two cause its related to it. lots of proofs uses number theory. – DeepSea May 09 '16 at 03:50

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A First Course In Abstract Algebra-John B. Fraleigh, 7Ed would be very good.

Simple
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