This chapter provides an overview of the fundamental properties and equations that form the basis for analyzing semiconductor devices. It begins with Poisson's equation, which is derived from Maxwell's equations and modified to suit semiconductor problems. The permittivity tensor is simplified to a scalar quantity for most materials used in device fabrication. The space charge density is expressed as a product of elementary charges, hole density, electron density, and an additional concentration term. Continuity equations are then derived from the first Maxwell equation, leading to two equations that describe the net generation and recombination of electrons and holes. The chapter also discusses carrier transport equations, which are derived from the Boltzmann transport equation. These equations describe the motion of charged particles in response to electric fields and internal forces, and they are essential for understanding the behavior of semiconductor devices. The chapter emphasizes the complexity of solving these equations analytically and the need for numerical methods, particularly in the context of modern device modeling.This chapter provides an overview of the fundamental properties and equations that form the basis for analyzing semiconductor devices. It begins with Poisson's equation, which is derived from Maxwell's equations and modified to suit semiconductor problems. The permittivity tensor is simplified to a scalar quantity for most materials used in device fabrication. The space charge density is expressed as a product of elementary charges, hole density, electron density, and an additional concentration term. Continuity equations are then derived from the first Maxwell equation, leading to two equations that describe the net generation and recombination of electrons and holes. The chapter also discusses carrier transport equations, which are derived from the Boltzmann transport equation. These equations describe the motion of charged particles in response to electric fields and internal forces, and they are essential for understanding the behavior of semiconductor devices. The chapter emphasizes the complexity of solving these equations analytically and the need for numerical methods, particularly in the context of modern device modeling.