Daniel Huybrechts is Professor in the Mathematical Institute at the University of Bonn. Manfred Lehn is Professor in the Mathematical Institute at Johannes Gutenberg University, Mainz, Germany.

• Preface to the second edition; Preface to the first edition; Introduction; Part I. General Theory: 1. Preliminaries; 2. Families of sheaves; 3. The Grauert–Müllich Theorem; 4. Moduli spaces; Part II. Sheaves on Surfaces: 5. Construction methods; 6. Moduli spaces on K3 surfaces; 7. Restriction of sheaves to curves; 8. Line bundles on the moduli space; 9. Irreducibility and smoothness; 10. Symplectic structures; 11. Birational properties; Glossary of notations; References; Index.

'The authors have created a true masterpiece of mathematical exposition. Bringing together disparate ideas developed gradually over the last fifty years into a cohesive whole, Huybrechts and Lehn provide a compelling and comprehensive view of an essential topic in algebraic geometry. The new edition is full of gems that have been discovered since the first edition. This inspiring book belongs in the hands of any mathematician who has ever encountered a vector bundle on an algebraic variety.' Max Lieblich, University of Washington