This volume presents twenty-three selected survey articles on central topics of geometric analysis and general relativity, written by prominent experts in the fields. Topics of geometric analysis include: the Yamabe problem, mean curvature flow, minimal surfaces, harmonic maps, Ricci flow, gluing and desingularisation constructions, function theory, collapsing of manifolds, Kähler-Einstein metrics, asymptotic geometry of complete manifolds, and the geometry of Teichmüller spaces. General relativity topics include: the positive mass theorem, the Penrose inequality, scalar curvature and Einstein's constraint equations, quasi-local mass functionals, the topology of higher dimensional black holes, and the positive mass theorem for asymptotically hyperbolic manifolds.