The authors of this book have endeavoured to give an overview of the techniques, which operate at various levels of sophistication to describe microscopic and macroscopic properties of wide range of materials. The most important methods used today in computational physics are addressed and, in general, each topic is illustrated by a number of applications. The book starts with basic aspects of density functional theory and the discussion of modern methods to calculate the electronic structure of materials. A rapidly developing field of scientific interest over the last years is nanophotonics. Two articles discuss how properties of photonic nanostructures can be computed. The main part of the book contains contributions dealing with different aspects of simulation methods. Ab initio calculations of free and supported molecules and clusters are discussed. The application of molecular-dynamics in biology, chemistry and physics is studied. The articles give a representative cross section of different simulation methods on the one hand and of their application to different materials on the other hand. Essential for the field of the Computational Material Science is the availability of effective algorithms and numerical methods. Therefore multigrid methods and strategies for the implementation of sparse and irregular algorithms are discussed as well.