The past ten years or so have seen the emergence of a new mathematical subject which now bears the name Homological Algebra. To begin with, it was the concern of a few enthusiasts in certain specialized fields but, since the publication of Cartan and Eilenberg's now famous book, its importance for several of the main branches of pure mathematics has been generally recognized.

The young mathematician, about to start on research, will be anxious to learn about homological ideas and methods, and one of the aims of this book is to help him to get started. In trying to cater for his needs, I have imagined such a reader as being familiar with the notions of group, ring and field but still relatively inexperienced in modern algebra. For him, the account given here is self-contained save in a small number of particulars which are mentioned below, and which need not discourage him.

An introduction to homological algebra must, of necessity, be an introduction to the book of Cartan and Eilenberg, for the student who wishes to go further will need to read their work; but much of great interest and value has been achieved even more recently, and some of this later work has been given a place in the following pages. The list of contents gives a fairly detailed picture of the main topics treated, but a few additional comments may be a help.

Chapters 1–6 develop, in a leisurely manner, the results that are needed to establish and illustrate the theory of derived functors, after which follows an account of torsion and extension functors.