1 Special Relativity, Lorentz transformations, Minkowski Geometry 2 Differential Geometry, Manifolds, Vector fields and Lie-derivative, Tensor fields, Differential forms 3 Metric Geometry, Parallel transport, Curvature, Geodesic and Deviation equation, Cartans vector-valued forms 4 Equivalence principle and Einstein's field equations, Newtonian limit 6 Killing vectors and symmetries, Schwarzschild geometry,Black holes 7 Experimental tests, Lightlike and timelike geodesics, Bending of light and Perihelion precession
R Wald, General Relativity
Misner,Thorne and Wheeler, Gravitation