This book presents the proceedings of the international workshop, ``Advances in Mathematical Analysis of Partial Differential Equations' held at the Institut Mittag-Leffler, Stockholm, Sweden, July 9-13, 2012, dedicated to the memory of the outstanding Russian mathematician Olga A. Ladyzhenskaya. The volume contains papers that engage a wide set of modern topics in the theory of linear and nonlinear partial differential equations and applications, including variational and free boundary problems, mathematical problems of hydrodynamics, and magneto-geostrophic equations.