This course will lay out the tools and fundamentals essential to carry out modeling, computation, analysis of flow at a pore scale. In particular, numerical techniques used to solving Stokes and Navier-Stokes within the framework of staggered-grid finite-difference methods will be introduced. The student will learn the basic principle of multiphase flow at a pore scale as well as its numerical modeling. Pore-scale flow and transport in geological formation and its applications to oil industry problems will be emphasized.