Michael Potter presents a comprehensive introduction to modern set theory, based on his 1990 book Sets but substantially revised and updated for a broad philosophical readership. It includes extensive coverage of cardinal and ordinal arithmetic, equivalents of the axiom of choice, and other axiom candidates such as determinacy. The project of set-theoretic reduction, which shows how we can interpret the rest of pure mathematics in set theory, is also discussed in detail. A central theme is the problem of assessing the significance of this reduction.