# 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slightly out of date.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.