This book presents a comprehensive overview of semiconductor equations, focusing on the hierarchy of models ranging from kinetic transport equations to drift diffusion equations. It is aimed at applied mathematicians, electrical engineers, and solid state physicists, with an accessible exposition for graduate students in each field. The authors emphasize the derivation of models and the physical and mathematical assumptions underlying them, rather than delving into the detailed mathematical technicalities. The book discusses the drift diffusion model, which is widely used for simulating semiconductor devices, and highlights its limitations in modeling ultra-integrated devices. Extensions of the drift diffusion model, such as hydrodynamic models, are explored for modeling hot electron effects in submicron MOS-transistors. Kinetic models, including semiclassical Boltzmann-Poisson and Wigner-Poisson equations, are also considered for highly integrated devices. The book covers various models, including kinetic transport models, hydrodynamic models, and drift diffusion equations, along with their applications in semiconductor devices such as P-N diodes, bipolar transistors, PIN-diodes, thyristors, MIS-diodes, and MOSFETs. It also discusses the derivation of the drift diffusion equations, their existence and uniqueness, and their application in different device configurations. The book includes problems and references for further study. The authors acknowledge the support of various funding bodies and institutions, and thank colleagues and readers for their contributions. The book is structured into chapters covering kinetic transport models, fluid dynamical models, drift diffusion equations, and device applications.This book presents a comprehensive overview of semiconductor equations, focusing on the hierarchy of models ranging from kinetic transport equations to drift diffusion equations. It is aimed at applied mathematicians, electrical engineers, and solid state physicists, with an accessible exposition for graduate students in each field. The authors emphasize the derivation of models and the physical and mathematical assumptions underlying them, rather than delving into the detailed mathematical technicalities. The book discusses the drift diffusion model, which is widely used for simulating semiconductor devices, and highlights its limitations in modeling ultra-integrated devices. Extensions of the drift diffusion model, such as hydrodynamic models, are explored for modeling hot electron effects in submicron MOS-transistors. Kinetic models, including semiclassical Boltzmann-Poisson and Wigner-Poisson equations, are also considered for highly integrated devices. The book covers various models, including kinetic transport models, hydrodynamic models, and drift diffusion equations, along with their applications in semiconductor devices such as P-N diodes, bipolar transistors, PIN-diodes, thyristors, MIS-diodes, and MOSFETs. It also discusses the derivation of the drift diffusion equations, their existence and uniqueness, and their application in different device configurations. The book includes problems and references for further study. The authors acknowledge the support of various funding bodies and institutions, and thank colleagues and readers for their contributions. The book is structured into chapters covering kinetic transport models, fluid dynamical models, drift diffusion equations, and device applications.