Quantum physics is currently the best tested theory of nature. It is the basis for our understanding of fundamental processes at the single particle level up to complex systems in atomic, molecular and condensed matter physics. Its current status of perfection now allows the investigation of various new technologies from quantum information devices and quantum communication protocols over new neutron techniques, atom chips and molecular manipulation methods to quantum dots and quantum cascade lasers. The Vienna graduate school on complex quantum systems will provide a new generation of young researchers with a broad and comprehensive view on modern quantum physics and it will allow them to become specialists in cutting edge technologies. The graduate school will form a centre of excellence for students who will be selected from all over the world. Their teachers lead highly competitive groups, which are recognized as pioneers in various fields of quantum research. A number of lectures by distinguished visiting professors, regular summer schools, annual retreats as well as secondments to partner groups on all continents will complete the challenging educational program. In addition, the graduate school will strongly support opportunities for the students to improve their soft skills - such as for instance through courses on presentation techniques, scientific writing, English and research management. The graduate school is located at and jointly hosted by the University of Vienna and the Technical University of Vienna. It has additional partners at the University of Innsbruck. Website: http://www.coqus.at/