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.

This volume is dedicated to Richard Schoen—in honour of his contributions to both geometric analysis and general relativity. It is intended for both researchers and graduate students working in those fields.