Superfluids are distinguished from normal fluids by their ability to support a dissipationless flow. Such persistent currents are intimately related to the existence of vortices, which are localized phase singularities with a quantized circulation around a closed contour. Thus, they represent topological excitations which have a plethora of intriguing properties. The Intensive Week at Technische Universität Kaiserslautern (Germany) provides an in-depth introduction to the vortex physics in the realm of ultracold quantum gases, which consist of atoms or photons. Pedagogical lectures provide a concise overview about various vortex phenomena. Furthermore, the participants receive insightful exercise problems, which are solved in small working groups and whose solutions are afterwards discussed in plenum. The Intensive Week is kindly supported by the Collaborative Research Center SFB/TR 185 "OSCAR": Open System Control of Atomic and Photonic Matter.