Filtration in Porous Media and Industrial Application : Lectures given at the 4th Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Cetraro Italy August 24–29 1998 This book is devoted to the presentation of some flow problems in porous media having relevant industrial applications. The main topics covered are: the manufacturing of composite materials the espresso coffee brewing process the filtration of liquids through diapers various questions about flow problems in oil reservoirs and the theory of homogenization. The aim is to show that filtration problems arising in very practical industrial context exhibit interesting and highly nontrivial mathematical aspects. Thus the style of the book is mathematically rigorous but specifically oriented towards applications so that it is intended for both applied mathematicians and researchers in various areas of technological interest. The reader is required to have a good knowledge of the classical theory of PDE and basic functional analysis. Some general facts about filtration through porous media Numerical solution of reservoir flow models based on large time step operator splitting algorithms Filtration problems in various industrial processes Homogenization theory and applications to filtration through porous media.