The Quantum Chaos Group studies manifestations of classical chaos in properties of the corresponding quantum or more generally wave-dynamical systems. Such systems include microwave networks and cavities resonators, quantum graphs and billiards as well as atoms in strong electromagnetic fields. Properties of microwave and quantum graphs, and billiards depend very sensitively on the shapes of the systems and their classical analogues can exhibit chaotic, regular or mixed dynamics. We investigate quantum graphs and billiards in analog experiments using microwave networks and thin microwave resonators of corresponding shapes. Our experimental and theoretical investigations include the study of the statistical fluctuation properties of the eigenvalues, the manifestation of periodic orbits in quantum spectra, quantum chaotic scattering and isoscattering networks and graphs.