Volume II: The Proper Forcing Axiom (J T Moore); Tensor Triangular Geometry (P Balmer); The Emerging p-adic Langlands Programme (C Breuil); The Tangent Space to an Enumerative Problem (P Belkale); Scalar Curvature, Conformal Geometry, and the Ricci Flow with Surgery (F C Marques); Fukaya Categories and Bordered Heegaard-Floer Homology (D Auroux); Volume III: Quasi-isometric Rigidity of Solvable Groups (A Eskin & D Fisher); Differentiability of Lipschitz Functions, Structure of Null Sets, and Other Problems(M Csornyei et al.); Group Actions on Operator Algebras (M Izumi); Green Bundles and Related Topics (M-C Arnaud); A Hyperbolic Dispersion Estimate, with Applications to the Linear Schrodinger Equation (N Anantharaman et al.); Topological Field Theory, Higher Categories, and Their Applications (A Kapustin); Volume IV: Random Planar Metrics (I Benjamini); Flag Enumeration in Polytopes, Eulerian Partially Ordered Sets and Coxeter Groups (L J Billera); Smoothed Analysis of Condition Numbers (P Burgisser); The Hybridizable Discontinuous Galerkin Methods (B Cockburn); Optimal Control under State Constraints (H Frankowska); Deterministic and Stochastic Aspects of Single-crossover Recombination (E Baake); Professional Knowledge Matters in Mathematics Teaching (J Adler); History of Convexity and Mathematical Programming: Connections and Relationships in Two Episodes of Research in Pure and Applied Mathematics of the 20th Century (T H Kjeldsen); and other papers.