Lorentz geometry -- Special Relativity -- General relativity and Einstein's equations -- Schwarzschild spacetime and black holes -- Cosmology -- Local Cauchy problem -- Constraints -- Relativistic fluids -- Relativistic kinetic theory -- Progressive waves -- Global hyperbolicity and causality -- Singularities -- Stationary spacetimes and black holes -- Global existence theorems : asymptotically Euclidean data -- Global existence theorems : the cosmological case -- Appendices. Sobolev spaces on Riemannian manifolds ; Second-order elliptic systems on Riemannian manifolds ; Quasi-diagonal, quasi-linear, second-order hyperbolic systems ; General hyperbolic systems ; Cauchy-Kovalevski and Fuchs theorems ; Conform,l methods ; Kaluza-Klein theories -- Related papers. Causality of classical supergravity ; Gravitation with gauss bonnet terms ; Interaction of gravitational and fluid waves ; Positive-energy theorenis