This volume contains the lectures presented at the NATO ADVANCED STUDY INSTITUTE that took place at Newark, Delaware, U. S. A. , July 14-23, 1985. The objective of this meeting was to present and discuss selected topics associated with transport phenomena in porous media. By their very nature, porous media and phenomena of transport of extensive quantities that take place in them, are very complex. The solid matrix may be rigid, or deformable (elastically, or following some other constitutive relation), the void space may be occupied by one or more fluid phases. Each fluid phase may be composed of more than one component, with the various components capable of interacting among themselves and/or with the solid matrix. The transport process may be isothermal or non-isothermal, with or without phase changes. Porous medium domains in which extensive quantities, such as mass of a fluid phase, component of a fluid phase, or heat of the porous medium as a whole, are being transported occur in the practice in a variety of disciplines.