This volume contains contributions from speakers at the 4th International Symposium on Finite Volumes for Complex Applications, held in Marrakech, Morocco, in July 2005. The subject of these papers ranges from theoretical and numerical results to physical applications.Topics covered include:Theoretical and numerical results? theoretical foundation? convergence? new finite volume schemes? adaptivity? higher order discretization and parallelizationPhysical applications? multiphase flow and flows through porous media? turbulent flows? shallow water problems? stiff source terms? cryogenic applications? medical and biological applications? image processingPapers on Industrial codes, as well as interdisciplinary approaches are also included in these proceedings.