Over the past century, our more and more refined understanding of light-matter interactions at the level of single atoms and photons has led to ultra-precise tests of quantum mechanical principles and groundbreaking innovations such as the laser or atomic clocks. Today, these quantum optical concepts also find wide-spread applications in the modelling of coherent solid-state systems, such as superconducting circuits, quantum dots or even macroscopic mechanical resonators, and are the basis for many developments in the emerging field of quantum technologies. This course introduces the basic theoretical tools that are required to model quantum light-matter interactions and open quantum systems in general and discusses their application for describing essential quantum optical effects, ranging from Rabi oscillation to laser cooling techniques and the generation of nonclassical photon pairs. The following main topics are covered in this course:-) semi-classical light-matter interactions -) quantum states of light-) cavity QED and the Jaynes-Cummings model-) open quantum systems and the master equation -) mechanical effects of light: laser cooling and trapping-) quantum Langevin equations-) optomechanical systems-) EIT and slow light-) photodetection and correlations-) non-linear optical processes-) phase space methods-) laser theoryThe main course will be complemented by an exercise course, where, in particular, students will be introduced to numerical solutions of quantum optical problems using Python.