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I am an undergraduate student - just started to learn about group theory, ring theory and module theory. I am self studying from the book "Basic Abstract Algebra" by P.B.Bhattacharya, S.K.Jain, S.R.Nagpaul. Prof said that this book is written in an uncomplicated manner but i found the statements in it with more hints rather than complete proofs. What are your thoughts about this book? Our prof also suggested Abstract Algebra by Dummit and Foote - but i found it quite bulky. Please enlighten me with your thoughts as i am very much lost - which one to follow. Thank you.

user26857
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Ankur Garg
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    Dummit and Foote might be bulky, but it's very readable and comprehensive. Don't focus on going through everything: I still haven't finished the whole book, despite learning A.A years ago. – Rushabh Mehta May 20 '21 at 15:26
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    Dummit & Foote is pretty good. You also have the books by Hungerford, Gallian, Herstein . Now, whatever you do do not read Lang's book. This is a very good consult book but rather for graduate level. – DonAntonio May 20 '21 at 15:29
  • @DonAntonio I remember seeing a thread similar to this a few years ago with someone recommending a new undergrad Lang. That was hilarious. – Rushabh Mehta May 20 '21 at 15:36
  • @Don, Well, I was referring above to Lang's "Algebra" . His "Undergraduate Algebra" seems to be way more accesible, but I don't know it very well. I know its "Algebra" and it can be pretty helpful...at a rather much higher level than first time undergraduates'. – DonAntonio May 20 '21 at 15:49
  • @DonAntonio Ahhh. Still, I contend that Lang's UA is still too much for a first year uni student, at least not one without prior experience in higher level maths. – Rushabh Mehta May 20 '21 at 15:53
  • @DonThousand Knowing several books by Lang, I wouldn't doubt that at all. – DonAntonio May 20 '21 at 15:57
  • Personally, I really like the style of Aluffi's Algebra, Chapter 0 book. – George Giapitzakis May 20 '21 at 16:02

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Dummit and Foote. Its bulkiness means it'll serve you well for years. It's detailed, patient, logical, and comprehensive. Some of its later material isn't great in my opinion, like its treatment of homological algebra with basically no motivation or punchline, but few people make it there anyway. Its character theory is actually quite good too.

Joshua P. Swanson
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