In this course we will discuss the quantum properties of light and aim to provide the students with the means to mathematically describe quantum optical fields and states as well as the interaction between light and matter. Topics include: interferometric measurements, measurement noise, photon statistics, non-classical states of light (single-photon sources, squeezed light), cavity quantum electrodynamics (cavity QED), quantum optical control of matter (trapped ions/atoms, quantum optomechanics), measuring time and space with quantum light (frequency combs, atomic clocks, gravitational-wave detectors), quantum entanglement, applications of quantum optics