ContentsOn the conformal scalar curvature equation and related problems (by S. Brendle)A survey of the Kähler-Ricci Flow and Yau's Uniformization Conjecture (by A. Chau, L.-F. Tam)Recent developments on the Hamilton's Ricci Flow (by H.-D. Cao, B.-L. Chen, and X.-P. Zhu)Curvature flows in semi-Riemannian manifolds (by C. Gerhardt)Global regularity and singularity development for wave maps (by J. Krieger)Relativistic Teichmüller theory: a Hamilton-Jacobi approach to 2+1-dimensional Einstein gravity (by V. Moncrief)Monotonicity and Li-Yau-Hamilton inequalities (by L. Ni)Singularities of mean curvature flow and flow with surgeries (by C. Sinestrari)Some recent developments in Lagrangian mean curvature flows (by M.-T. Wang)