Let us recall some classic words:

Our subject starts with homology, homomorphisms, and tensors.

Saunders Mac Lane, in "Homology"

And while Mac Lane's "Homology" and its friend by Cartan and Eilenberg are certainly fairly comprehensive sources of homological algebra, viewpoint shifts in the subject have made more recent approaches desirable. Weibel's 'An Introduction to Homological Algebra' (author website, Amazon), or IHA, is just that: a modern textbook on homological algebra. Aside from a few busy semesters, during the last two years I have been slowly reading it, as I was determined to read this book cover-to-cover. Now that I have finished this, it is my pleasure to write a short review of this book.

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