Invited Lectures: A level set method for the numerical simulation of damage evolution by G. Allaire, F. Jouve, and N. Van Goethem Dissipation inequalities in systems theory: An introduction and recent results by C. Ebenbauer, T. Raff, and F. Allgower Some nonlinear problems involving non-local diffusions by L. Caffarelli High-order methods for PDEs: Recent advances and new perspectives by C. Canuto Radar imaging by M. Cheney Adaptive approximations by greedy algorithms by A. Cohen Multiscale analysis of density functional theory by Weinan E Frictional contact in solid mechanics by M. Fortin, C. Robitaille, A. Fortin, and A. Rezgui Numerical methods for fully nonlinear elliptic equations by R. Glowinski Asymptotic solutions of Hamilton-Jacobi equations for large time and related topics by H. Ishii Hyperbolic conservation laws. Past and future by B. Keyfitz Second-order PDE and deterministic games by R. Kohn and S. Serfaty Controllability and observability: From ODEs to quasilinear hyperbolic systems by T. Li Order-value optimization and new applications by J. Martinez Conformation dynamics by C. Schutte, F. Noe, E. Meerbach, P. Metzner, and C. Hartmann MCMC methods for sampling function space by A. Beskos and A. Stuart Chaotic itinerancy reality in the dynamic brain — episodic memory formation by I. Tsuda Visibility and invisibility by G. Uhlmann Optimal algorithms for discretized partial differential equations by J. Xu Euler Special Lecture: Leonhard Euler: His life, the man, and his works by W. Gautschi