Upper mass limit for relativistic stars. Schwarzschild black hole. Gravitational collapse. The initial value problem. Strong cosmic censorship. Causal structure. Null geodesic congruences. Penrose singularity theorem. Penrose diagrams. Asymptotic flatness. Weak cosmic censorship. Reissner-Nordstrom and Kerr black holes. Energy, angular momentum and charge in curved spacetime. The laws of black hole mechanics. The analogy with the laws of thermodynamics. Quantum field theory in curved spacetime. The Hawking effect and its implications.