Basic Laws and Models for Flow in Porous Media. Generalities. The Geometry of the Field. The Basic Laws for One and Two-Phase Flow. The Basic Models. Qualitative Behavior of the Solution in the No-Diffusion and No-Capillary Pressure Case. Slightly Compressible Monophasic Fields. Construction of the Pressure Equation. Existence and Uniqueness Theorems. An Alternative Model of Monophasic Wells. Incompressible Two Phase Reservoirs. Construction of the State Equations. Summary of Equations of Two Phase Flows for Incompressible Fluids and Rock. An Alternative Model for Diphasic Wells. Mathematical Study of the Incompressible Two-Phase Flow Problems. The Case of Fields with Different Rock Types. Generalization to Compressible, Three Phase, Black Oil or Compositional Models. The Two-Phase Compressible Model. A Finite Element Method for Incompressible Two-Phase Flow. Approximation of the Pressure-Velocity Equations. Resolution of the Algebraic System for Pressure-Velocity. Approximation of the One-Dimensional Saturation Equation: The Case with Neither Capillary Pressure Nor Gravity. Approximation of the One-Dimensional Saturation Equation in the General Case. Approximation of the Saturation Equation in Two Dimensions.