A self-contained introduction to the mathematical theory of black holes.
1. Preliminaries; 2. Spacetimes admitting killing fields; 3. Circular spacetimes; 4. The Kerr metric; 5. Electrovac spacetimes with killing fields; 6. Stationary black holes; 7. The laws of black hole physics; 8. Integrability and divergence identities; 9. Uniqueness theorems for nonrotating holes; 10. Uniqueness theorems for rotating holes; 11. Scalar mappings; 12. Self-gravitating harmonic mappings; References; Subject index.