QMath9 is a meeting for young scientists to learn about the state of the art in the Mathematical Physics of Quantum Systems. This selection of outstanding articles written in pedagocical style has six sections that cover new techniques and recent results on spectral theory, statistical mechanics, Bose-Einstein condensation, random operators, magnetic Schrödinger operators and much more. For postgraduate students this book can be used as a useful introduction to the research literature. For more expert researcher this book will be a concise and modern source of reference.