The unifying methodological approaches of our research are: emphasising the underlying structure of a given problem, taking the geometric viewpoint when looking at problems and studying the relevant dynamics of group or semigroup actions. They are a coherent bracket around all projects of Mathematics Münster. Our research programme focuses on three major research areas, namely Arithmetic and Groups (A), Spaces and Operators (B), and Models and Approximations (C), which are unified by the three approaches, Dynamics, Geometry and Structure.