The aim of the meeting is to present the state of the art in some challenging open problems in Quantum Mechanics from the point of view of Mathematical Physics. It is addressed to young people interested in working on the subject but also to experienced researchers willing to exchange the newest ideas and methods in the field. Among the topics covered: spectral and scattering theory for Schrödinger operators, effective behavior in many particles quantum systems, Bose-Einstein condensation, nonlinear Schrödinger equation, semiclassical analysis, numerical analysis of quantum systems, quantum graphs. Three courses of 6 hours will be given in a series of lectures scheduled in the morning of each day. In the afternoon short contributed talks will be given by young participants, followed by plenary talks given by invited speakers.