The program was timely because the subject is undergoing very rapid development at present, in both communities. In the mathematical analysis of the Einstein equations, major progress has been achieved in the last ten years or so and certain old and central open questions now seem within reach. On the physical side the imminent detection of gravitational waves (by earth-based detectors like LIGO/VIRGO/KAGRA) or through a pulsar timing array (e.g. NANOGRAV), as well as the advent of Very-Long-Baseline interferometry capable of providing images with horizon scales for the supermassive black holes at the center of our galaxy and Andromeda, will provide unprecedented opportunities to put General Relativity to stringent tests. Additionally, this last decade has witnessed an explosion of activities connecting gravitation in asymptotically anti-de Sitter spacetimes to field theories on the spacetime’s causal boundary through the so-called holographic duality. Finally, the observation that our universe seems filled with dark energy (perhaps in the form of Einstein’s cosmological constant) raises serious questions as to whether General Relativity is indeed the correct description of gravitation, or whether it should be replaced by an alternative theory. Proposals to replace General Relativity abound, but their mathematical properties are typically delicate at best, and largely unexplored.