In 2003 the XIV International Congress on Mathematical Physics (ICMP) was held in Lisbon with more than 500 participants. Twelve plenary talks were given in various fields of Mathematical Physics: E Carlen "On the relation between the Master equation and the Boltzmann Equation in Kinetic Theory"; A Chenciner "Symmetries and "simple" solutions of the classical n-body problem"; M J Esteban "Relativistic models in atomic and molecular physics"; K Fredenhagen "Locally covariant quantum field theory"; K Gawedzki "Simple models of turbulent transport"; I Krichever "Algebraic versus Liouville integrability of the soliton systems"; R V Moody "Long-range order and diffraction in mathematical quasicrystals"; S Smirnov "Critical percolation and conformal invariance"; J P Solovej "The energy of charged matter"; V Schomerus "Strings through the microscope"; C Villani "Entropy production and convergence to equilibrium for the Boltzmann equation"; D Voiculescu "Aspects of free probability".The book collects as well carefully selected invited Session Talks in: Dynamical Systems, Integrable Systems and Random Matrix Theory, Condensed Matter Physics, Equilibrium Statistical Mechanics, Quantum Field Theory, Operator Algebras and Quantum Information, String and M Theory, Fluid Dynamics and Nonlinear PDE, General Relativity, Nonequilibrium Statistical Mechanics, Quantum Mechanics and Spectral Theory, Path Integrals and Stochastic Analysis.