Our team studies the quantum properties of novel micro- and nano-structured electronic devices and their interaction with classical and quantum electromagnetic fields in a state-of-the-art research environment. Our research is positioned at the intersections of mesoscopic condensed matter physics, atomic physics and quantum optics, where physical systems with intriguing properties and exciting applications can be realized. As one focus topic, we study the fundamental physics of matter/light interaction in the context of cavity quantum electrodynamics (QED). The strong coherent coupling between a single quantum two-level system and a single mode of a quantized electromagnetic field allows us to explore interactions in solid-state electronic circuits on the single photon level. This field of research founded in 2004 is now known as circuit quantum electrodynamics, or short Circuit QED. Circuit QED has enabled the study of a wide range of quantum optical phenomena in superconducting electronics circuits at a level of detail and control which rivals approaches in other physical systems, such as atoms, molecules, semi-conductor quantum dots or nitrogen-vacancy centers. Commonly, in circuit QED the quantum physics of radiation fields localized in transmission line cavities is investigated through its interaction with individual or collections of non-linear superconducting multi-level systems. In addition, pioneering work performed in our laboratory since 2010 has for the first time enabled the detailed study of quantum properties of propagating microwave fields. Instead of using photo-detectors, ubiquitous at optical frequencies, we instantaneously detect amplitude and phase of propagating quantum fields versus time, which we first amplify using linear or parametric amplifiers. We are then able to measure higher order correlation functions and to perform full quantum state tomography on propagating modes, even in the presence of significant noise added by the amplifiers. In the context of quantum information science, we control the dynamics of quantum systems, consisting of a larger number of qubits, to investigate complex physical and computational problems. Our approach is based on coherently controlling the dynamics of superconducting quantum electronic circuits using amplitude and phase controlled pulsed microwaves. In particular we investigate non-classical correlations as they are generated in strong coherent interactions between quantum systems, giving rise to their entanglement. We also make use of such entangled states to realize quantum algorithms such as teleportation. Since 2009, we have begun to explore the use of circuit QED techniques in collaboration with partners from different departments. We have had first success in the realization of hybrid quantum systems in which we, for example, control and detect the quantum properties of semiconductor quantum dots or Rydberg atoms. In an effort to develop novel measurement and instrumentation technologies, we realize applications of quantum electronic circuits as sensitive, possibly quantum limited, nano-electronic measurement devices and detectors. In particular, we have recently successfully developed parametric amplifiers and digital electronics to perform real-time analysis of acquired data at very high sustained data rates.