We are the Cluster of Excellence ct.qmat – Complexity and Topology in Quantum Matter. Established in 2019, the Würzburg-Dresden Cluster ct.qmat is a leading international center for research on topological and complex quantum matter. Our aim is to develop a deep understanding of quantum phenomena in general and to identify materials in which those phenomena are observed in the laboratory. This is supported by educating and attracting top-level students and scientists as well as by supplementing infrastructure in both Würzburg and Dresden.