This book is the first one that combines both research in multigrid methods and a particular application field here - process simulation. It is the declared intention of this book to convince by practically demonstrating the power of the multigrid principle and to establish an example of fruitful interdisciplinary interaction. The introduction to multigrid is therefore strictly directed towards the goal to provide the algorithmical overview one needs to compose optimal multigrid algorithms for evolution problems of process simulation and similar applications. The necessary explanation how and why multigrid works is derived from the roots. So the book preassumes no advanced familiarity with numerical analysis. Additionally a complete strategy to implement different algorithmical components on an adaptive multilevel grid structure is presented. The outlined principle of grid definement and adaption is based on the control of errors and is reliable as well as general. Last but not least the described strategies are applied to "real life" problems of process simulation. Consequently this book is an important contribution to the interdisciplinary challenge of improving numerical techniques for diffusion problems of process simulation.