The International Congress on Mathematical Physics is the flagship conference in this exciting field. Convening every three years, it gives a survey on the progress achieved in all branches of mathematical physics. It also provides a superb platform to discuss challenges and new ideas. The present volume collects material from the XVIth ICMP which was held in Prague, August 2009, and features most of the plenary lectures and invited lectures in topical sessions as well as information on other parts of the congress program.This volume provides a broad coverage of the field of mathematical physics, from dominantly mathematical subjects to particle physics, condensed matter, and application of mathematical physics methods in various areas such as astrophysics and ecology, amongst others.Contents:Dynamical Systems (Including Integrals Systems and Hamiltonian Stability)Equilibrium Statistical Mechanics (Classical and Quantum)Non-Equilibrium Statistical Mechanics (Including Stochastic Evolutions Except SLE and Boltzmann Equation)PDE's (Fluid Dynamics, Wave Equation and NLSE, Boltzmann Equation, General Relativity, and Elasticity)Probability Theory (Including Random Matrices and SLE)Operator Algebras (Including Noncommutative Geometry)Nonrelativistic Quantum Mechanics (Including Quantum Information)String Theory and Quantum GravityQuantum Field Theory (Including Field Theoretical Methods in Condensed Matter)Many-Body Quantum Mechanics (Condensed Matter, Nanoscale, Elasticity)New Frontiers in Mathematical Physicsand related topicsReadership: Students, researchers and professionals in mathematical physics.