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Abstract Algebra seems to be a huge topic that I'd like to study in some depth. Is there some series of books on algebra that starts from an (upper-division) undergrad level and includes a fairly comprehensive subject list -- including (amongst all the basics like groups/ rings/ fields) introductions to topics like algebras over fields/ rings, lattices, homological algebras, algebraic geometry, topological algebra, etc?

I'm looking for a series of books in the same vein as Spivak's A Comprehensive Introduction to Differential Geometry and the Princeton Lectures on Analysis.

If no such good series exists for abstract algebra, is Dummit/ Foote the most comprehensive single textbook that you guys know of? I'm looking to spend a year or two going through the material so it doesn't matter if it's really long.

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  • $\begingroup$ You could try Serge Lang's book $\endgroup$
    – R_D
    Nov 12, 2015 at 4:14
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    $\begingroup$ Jacobson has a famous 3-volume series "Lectures in Abstract Algebra". These are probably dated (1950-60s), but I have heard good things about them. $\endgroup$
    – darij grinberg
    Nov 12, 2015 at 4:33
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    $\begingroup$ Do not try Lang unless you like correcting errors and filling gaps in proofs :) $\endgroup$
    – darij grinberg
    Nov 12, 2015 at 4:34
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    $\begingroup$ Rotman's 1000-page "Advanced Modern Algebra" might cover a lot of what you want your series to do. $\endgroup$
    – darij grinberg
    Nov 12, 2015 at 4:35
  • $\begingroup$ Bourbaki's 2-volume algebra $\endgroup$
    – WWK
    Nov 12, 2015 at 4:40

2 Answers 2

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Abstract Algebra by IN Herstein.

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There is the two-volume set Basic Algebra by Jacobson.

They have been reprinted by Dover: volume 1 and volume 2.

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