This book is intended for one-quarter, two-quarter, or one-semester courses in homological algebra. The aim is to cover Ext and Tor early and without distraction. It includes several further topics, which can be pursued independently of each other. Many of these, such as Lazard's theorem, long exact sequences in Abelian categories, the Ext product, or the relation between Krull dimension and global dimension, are hard to find elsewhere. The intended audience is second- or third-year graduate students in algebra, algebraic topology, or any other field that uses homological algebra.