Numerical simulation models have become indispensable in hydro- and environmental sciences and engineering. This monograph presents a general introduction to numerical simulation in environment water, the basic equations for groundwater flow and transport processes, for multiphase and multicomponent flow and transport processes in the subsurface as well as for flow and transport processes in surface waters. It displays the state of the art of discretization and stabilization methods (e.g. Finite-Difference, Finite-Element and Finite-Volume Methods), parallel methods and adaptive methods as well as fast solvers with particular focus on explaining the interactions of the different methods. The book gives an overview of various information-processing techniques and demonstrates the interactions of the numerical methods with the information-processing techniques in order to achieve efficient numerical simulations for a wide range of applications in environment water.