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This book gathersa collection of refereed articles containing original result srepo- ing the recent originalcontributions of the lectures and communications presented at the Free Boundary Problems (FBP2005) Conference that took place at the University of Coimbra, Portugal, from 7 to 12 of June 2005. They deal with the Mathematics of a broad class of models and problems involving nonlinear partial diferentialequationsarising inPhysics, Engineering, Biology and Finance. Among the main topics, the talks considered free boundary problems in biomedicine, in porous media, in thermodynamic modeling.