| Text | Target audience | Length | Style | Best for | |------|----------------|--------|-------|-----------| | | 1st-year grad | ~150 pp | Gentle, exercises | Basics: Noetherian rings, primary decomposition, completions | | Matsumura (CRT) | 2nd-year grad / researcher | 320 pp | Dense, encyclopedic | Flatness, regular rings, dimension, duality | | Eisenbud | Geometers | 800 pp | Chatty, many examples | Geometric intuition, homological methods | | Bruns–Herzog | Advanced researcher | ~400 pp | Terse, high-level | Cohen–Macaulay rings, canonical modules | | Stacks Project | Everyone | 7000+ pp | Open-source, hyperlinked | Comprehensive reference, always up-to-date |

Many graduate students and researchers keep this book on hand specifically for "hard" results that appear in algebraic geometry papers, such as:

The title is telling—this book shines most brilliantly in its treatment of .