The last few decades have seen the trend to extend the scope of classical analytic and geometric theories from the familiar Euclidean space or manifold setting to more general metric spaces, often of a non-smooth or fractal nature. Recently there has been spectacular progress on the development of a theory of general metric spaces resembling manifolds with Ricci curvature bounds by the work of Lott, Villani and Sturm. Their approach is based on convexity properties of an entropy functional in optimal transport. Other approaches include the use of Bochner type formulas by Baudoin and Garofalo and the use of heat kernels by Koskela, Rajala and Shanmugalingam and by Ambrosio, Gigli and Savare. However, many of the underlying analytic and geometric questions are still poorly understood. This workshop will further explore these approaches and related challenging issues, and foster new collaborations among various groups of researchers.