The topological symmetry in one and two space dimensions allows 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 at the Freie Universität Berlin (Germany) provides pedagogical introductory lectures into both anyon physics in general and their possible realization in the realm of ultracold quantum gases. Due to the support of the VolkswagenStiftung as well as the Sonderforschungsbereich/Transregio 49 this International School is the first one of three conferences on this intriguing topic, the subsequent ones are planned at the Technische Universität Kaiserslautern (Germany) in 2014 and in Uzbekistan in 2015.