The three-dimensional device simulation has become a necessary tool for the design and investigation of complex device structures. The evolution of the three-dimensional simulation tools is directly linked to the scaling of the devices and the increasing complex- ity of dynamic random access memory (DRAM) cells. Scaling of MOSFET devices led to a three-dimensional geometry with effects which cannot be handled by two-dimensional simulations anymore. With increasing integration density in DRAMs the third dimen- sion had to be utilized to realize the storage capacitor. The result- ing leakage problems have to be investigated and the cell design optimized by means of three-dimensional simulations. This book is intended for senior undergraduate students in applied physics, electrical engineering and computational physics, as well as for scientists and engineers involved in semiconductor device re- search and development. It is also intended for software engineers and all those who are concerned with simulation. The book will give an overview on the problems and activities con- cerning three-dimensional device simulation, without the claim of being a classical textbook. It starts from the classical semiconduc- tor equations, discusses the physical models used in device simu- lation, describes the discretization and some numerical methods for solving the differential equations. The application of the three- dimensional simulation to VLSI device engineering is illustrated by a few specific examples.