Combining theory and applications, this book deals with the modelling of materials properties and phenomena at atomic level. The first part provides an overview of the state of the art of computational solid state physics. Emphasis is given on the understanding of approximations and their consequences regarding the accuracy of the results. This part of the book also deals as a guide to find the best method for a given purpose. The second part offers a potpourri of interesting topical applications, showing what can be achieved by computational modelling. Here the possibilities and the limits of the methods are stressed. A CD-ROM supplies various demo programmes of applications.