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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.

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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. –  t.b. Mar 23 '11 at 11:23
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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)? –  Mark Mar 23 '11 at 19:57
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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. –  Sean Tilson Mar 23 '11 at 21:11
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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. –  JSchlather Mar 24 '11 at 2:09

2 Answers 2

up vote 5 down vote accepted

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.

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