General relativity and the Einstein equations - Choquet-Bruhat, Yvonne (Oxford mathematical monographs, 2009)
Lorentz geometry -- Special relativity -- General relativity and Einstein's equations -- Schwarzschild spacetime and black holes -- Cosmology -- Local cauchy problem -- Constraints -- Other hyperbolic-elliptic well-posed systems -- Relativistic fluids -- Relativistic kinetic theory -- Progressive waves -- Global hyperbolicity and causality -- Singularities -- Stationary spacetimes and black holes -- Global existence theorems asymptotically Euclidean -- Global existence theorems the cosmological -- 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 -- Conformal methods -- Kaluza-Klein theories.