The lectures presented in this book were delivered at the Colloquium "Mathematical Results in Statistical Mechanics", held in Marseilles, France in July 1998, as a satellite colloquium of the Paris conference STAPHYS 20. The lectures cover a large part of the contemporary results in statistical mechanics, from the point of view of mathematical physics, by leading experts in this field. It includes as the main topics, phase transitions, interfaces, disordered systems, Gibbsian and non-Gibbsian states, as well as rigorous treatments in quantum statistical mechanics.