ABSTRACT
Although General Relativity has roots on gravitational physics, its formulation relies on manifolds equipped with a Lorentzian metric satisfying the Einstein field equations, which are non-linear partial differential equations. This trigged the development of a new branch of Mathematics often called Mathematical Relativity. Landmarks of its history include the singularity theorems of Penrose and Hawking and the proof of stability of Minkowski space- time by Christodoulou and Klainerman. Remarkable progress has recently been made in the field including the Cauchy problem, stability of black holes, conformal methods, cosmic censorship and cosmic no-hair conjectures, some of which will be described in this talk.