Books on Homological Algebra
Hilton and Stammbach, A Course in Homological Algebra
(Springer Graduate Texts in Mathematics)
This was the nominal text for the course here.
I chose it because it was paperbound,
and I thought it would be a good reference for students to own.
It's a good textbook.
Joseph Rotman, Notes on Homological Algebra
This was probably the main model I used for the course.
Northcott, Introduction to Homological Algebra
This was the first book on homological algebra I ever read,
before I started graduate school.
It is one of the most readable texts available,
although some of the notation and terminology is now
slightly out of date.
MacLane, Homology
An excellent reference, and moderately readable.
The title is misleading, since no topological aspects of homology
are treated at all.
Cartan and Eilenberg, Homological Algebra
This was the book that started the whole subject, of course.
I remember how fascinated I was when I first saw it,
since it seemed intriguing that one could apply topology to algebra.
I wouldn't recommend that anyone start with this one,
but I actually found a number of useful facts here.
It should definitely not be considered obsolete.
Jans, Rings and Homology
A very small and somewhat intriguing book.
The first chapter gives a nice readable treatment
of the Wedderburn Theorem, suitable for beginners.
The reminder of the book is more specialized
and demands a greater sophistication from its readers.
Sharpe and Vamos, Injective Modules.
I like this little book a whole lot.
It brings in an assortment of subject matter
from a whole lot of ring theory,
both commutative and non-commutative,
and finishes up by giving the complete classification of
injective modules over commutative noetherian rings.
In my opinion, this is a good book from which to learn
what algebra, and in particular module theory, is all about.
Peter Freyd, Abelian Categories
This little book is what I learned my category theory from.
I found it fairly easy to read
once I learned to keep a pencil and paper handy,
so that for each sentence in the book
I could draw the corresponding diagram.
MacLane, Categories for the Working Man
This one is hard work, but worth it if you're seriously interested
in category theory.
The title (which I've actually misstated; but that's the way
I always think of it) is quite erroneous.
It should be called Categories for the Category Theorist.
Matsumuta, Commutative Algebra
This is certainly not an enjoyable book to read.
But at the time I taught the course,
it was the only book that treated most homological topics
in commutative ring theory.
There may be lots of more recent books which are excellent,
for all I know.
I basically lost interest in trying to keep up with these things
about twenty years ago.