The topological properties in one and two space dimensions allow for quantum particles to have a statistics, which can vary continuously from boson to fermion ones and is therefore called anyons. Such anyonic particles are becoming of increasing importance in condensed matter physics and quantum computation. They may play an essential role for describing the fractional quantum Hall effect, high-temperature superconductivity, and the physics of topological insulators and superconductors. Several proposals in the literature indicate the possibility to use the high degree of tunability of ultracold quantum gases as a quantum simulator in the sense of Richard Feynman in order to realize anyon physics. The International School and Workshop at the Technische Universität Kaiserslautern (Germany) provides pedagogical introductory lectures as well as research talks upon both anyon physics in general and their possible realization in the realm of ultracold quantum gases.