Advanced Topics in Computational Partial Differential Equations : Numerical Methods and Diffpack Programming The book is suitable for readers with a background in basic finite element and finite difference methods for partial differential equations who wants gentle introductions to advanced topics like parallel computing multigrid methods and special methods for systems of PDEs. The goal of all chapters is to *compute* solutions to problems hence algorithmic and software issues play a central role. All software examples use the Diffpack programming environment so to take advantage of these examples some experience with Diffpack is required. There are also some chapters covering complete applications i.e. the way from a model expressed as systems of PDEs through discretization methods algorithms software design verification and computational examples