The positive energy theorem and its extensions -- Mass and angular momentum at the quasi-local level in general relativity -- The positive mass theorem and black holes -- Exotic differentiable structures on Euclidean 4-space -- A new approach to the vacuum Einstein equation -- The existence of maximal surfaces in asymptotically flat spacetimes -- Causality of classical supergravity -- A gauge invariant index theorem for asymptotically flat manifolds -- On the boundary conditions for gravitational and gauge fields at spatial infinity -- Metric fluctuations and the entropy of black holes -- The numerical characteristic initial value problem -- Time-asymmetric initial data for n black holes -- The gravitational Hamiltonian -- Twistors, asymptotic symmetries and conservation laws at null and spatial infinity -- Two-surface twistors and conformal embedding -- Remarks on the cosmic censorship conjecture -- On some (con-)formal properties of Einstein's field equations and their consequences.