This book contains the proceedings of the QMath 7 Conference on Mathematical Results in Quantum Mechanics held in Prague, Czech Republic, from June 22 to 26, 1998. The purpose is to draw attention to recent developments in quantum mechanics stemming from its numerous applications, and to related mathematical problems and techniques. This volume is addressed to the broad audience of mathematicians and physicists interested in contemporary quantum physics and associated mathematical questions. The reader will find new results on Schrödinger and Pauli operators with regular, fractal or random potentials, scattering theory, adiabatic analysis, as well as on interesting new physical systems such as photonic crystals, quantum dots and wires