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I want a good Algebra book that covers some elementary algebra and some more advanced Algebra(i.e. Abstract Algebra, and maybe some other types, I don't know) Algebra. I found Gelfand's book Interesting for my level, I think it's not bad, it has some things I don't know well, but I know much of what is there. Any suggestion?

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    $\begingroup$ You should learn linear algebra before taking abstract algebra. $\endgroup$ Feb 2, 2020 at 16:30
  • $\begingroup$ Maybe Discourses on Algebra by Igor R. Shafarevich. I think most of the material in this book is freely available on the internet in the journal The Teaching of Mathematics (Belgrade, Serbia) --- see the links I posted in this answer. $\endgroup$ Feb 2, 2020 at 17:05
  • $\begingroup$ @DaveL.Renfro Oh, sounds very good. Could you tell me in a fast way the prerequisites, please? $\endgroup$
    – user743574
    Feb 2, 2020 at 17:36
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    $\begingroup$ The prerequisites will be much less than for Artin's Algebra or for Dummit/Foote's Abstract Algebra (neither of which is probably suitable for you now, in my opinion), but the Shafarevich book still might require (at least in some places) more than what you now know. I suspect you can answer your question much better than any of us by quickly looking over (by reading a few sentences here and there) the .pdf files whose links I give earlier -- click on "I posted in this answer" in my previous comment. $\endgroup$ Feb 2, 2020 at 18:24
  • $\begingroup$ @N.F.Taussig And... Linear Algebra after or before Calculus? $\endgroup$
    – user743574
    Feb 2, 2020 at 18:50

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I'd recommend Algebra by Michael Artin. Abstract Algebra by Dummit and Foote is also excellent, but it has a lot of material, so I don't think it's ideal for a first book on abstract algebra. Algebra by Michael Artin will get you through essential material quicker, so I think it's a better choice as a first book. Plus Algebra by Artin goes through a lot of fun non-standard topics. Both of these books are classics, and they're beautiful. So if you could get both, then that would be awesome. But if you had to pick one, I'd pick Algebra by Artin.

Edit: In the comments, someone recommended taking linear algebra before you learn abstract algebra. There is a lot of debate about this, with excellent points being made by both sides. For example: see this page. Another good thing about Algebra by Artin, is that it does a thorough job of covering a lot of linear algebra, early in the book.

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    $\begingroup$ Thanks so much for recommendations. Could I start Abstract Algebra, since I ended my last Algebra study at Bhaskara formula? In my class we did Bhaskara, Inequalities and some other Algebra. Maybe, still worth buying Gelfand's book on Algebra. I also saw that Artin's book versions I found and that were available for my country don't have the Galois Theory chapter. The only version that has the Galois Theory chapter isn't available for me, sadly. $\endgroup$
    – user743574
    Feb 2, 2020 at 17:43
  • $\begingroup$ I didn't know that there were versions that were missing the Galois Theory chapter. I think the book would still be a great first book on abstract algebra, even without that chapter. $\endgroup$
    – user729424
    Feb 2, 2020 at 18:00

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