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Which books would you recommend, for self-studying homological algebra, to a beginning graduate (or advanced undergraduate) student who has background in ring theory, modules, basic commutative algebra (some of Atiyah & Macdonald's book) and some (basic) field theory?

I would especially like to hear your opinions on the following books:

A Course On Homological Algebra / P. J Hilton and U. Stambach

Introduction to Homological Algebra / Szen-Tsen Hu

Notes on Homological Algebra / Rotman

But other recommendations will also be appreciated.

  • 4
    Weibel immediately comes to mind, it is a bit more advanced than the three books you mention. It's definitely worth looking into the eponymous Cartan-Eilenberg (the book that named and started the subject) and see how little has changed.2011-03-23
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    See http://mathoverflow.net/questions/2533/homological-algebra-texts2011-03-23
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    By the way, does anyone know of a homological algebra text which is elementary in the sense that it only discusses homology and cohomology for $\mathbb{Z}$-modules (i.e. abelian groups)?2011-03-23
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    Rotman has a larger book that I think is a better introduction to the subject. It is large, but rather nice.2011-03-23
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    Mildly off-topic, but: I just noticed this strange tag "self-learning". Is there some other kind of learning??2011-03-24
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    I think it just means that he intends on using the book purely on his own and not in conjunction with a course.2011-03-24
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    @Sean: probably this one: http://wwwdev.maa.org/maa%20reviews/01215.html2011-03-24
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    @Sean Complete agreement- Rotman's new edition of his classic is the definitive introduction for beginners to the subject.@t.b. Weibel is wonderful for it's modern, topologically rooted approach-but I think the average beginner is going to find it very tough going. I would recommend Rotman first, then Weibel.2011-11-07

2 Answers 2

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See also A first course of homological algebra by Northcott. There's a list in this review if you have access to MathSciNet.

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See "An introduction to homological algebra" of Rotman (2010). I think this is the book Mark was talking about. It is VERY introductory.