The complexity of Constraint Satisfaction Problems (CSPs) has become a major common research focus of graph theory, artificial intelligence, and finite model theory. A recently discovered connection between the complexity of CSPs on finite domains to central problems in universal algebra led to additional activity in the area.The goal of this project is to extend the powerful techniques for constraint satisfaction to CSPs with infinite domains. The generalization of CSPs to infinite domains enhances dramatically the range of computational problems that can be analyzed with tools from constraint satisfaction complexity. Many problems from areas that have so far seen no interaction with constraint satisfaction complexity theory can be formulated using infinite domains (and not with finite domains), e.g. in phylogenetic reconstruction, temporal and spatial reasoning, computer algebra, and operations research. It turns out that the search for systematic complexity classification in infinite domain constraint satisfaction often leads to fundamental algorithmic results.The generalization of constraint satisfaction to infinite domains poses several mathematical challenges: To make the universal algebraic approach work for infinite domain constraint satisfaction we need fundamental concepts from model theory. Luckily, the new mathematical challenges come together with additional strong tools, such as Ramsey theory or results from model theory. The most important challgenges are of an algorithmic nature: finding efficient algorithms for significant constraint languages, but also finding natural classes of problems that can be solved by a given algorithm.