This course gives an introduction to General Relativity from a mathematical point of view. Topics covered include the basic formulation of the theory, the black hole solutions of Schwarzschild and Kerr, the well-posedness of the Cauchy problem for the Einstein equations, Penrose's celebrated incompleteness theorems, and the formulation of the "cosmic censorship" conjectures. No prior background in the subject is required though basic differential geometry is assumed. Some experience with PDE's is also useful, but strictly speaking is not essential.