Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.

Daniel Huybrechts is a professor at the Mathematical Institute of the University of Bonn. He previously held positions at the Université Denis Diderot Paris 7 and the University of Cologne. He is interested in algebraic geometry, particularly special geometries with rich algebraic, analytic, and arithmetic structures. His current work focuses on K3 surfaces and higher dimensional analogues. He has published four books.

Preface; 1. Basic definitions; 2. Linear systems; 3. Hodge structures; 4. Kuga-Satake construction; 5. Moduli spaces of polarised K3 surfaces; 6. Periods; 7. Surjectivity of the period map and Global Torelli; 8. Ample cone and Kähler cone; 9. Vector bundles on K3 surfaces; 10. Moduli spaces of sheaves on K3 surfaces; 11. Elliptic K3 surfaces; 12. Chow ring and Grothendieck group; 13. Rational curves on K3 surfaces; 14. Lattices; 15. Automorphisms; 16. Derived categories; 17. Picard group; 18. Brauer group.