Although it has changed considerably in both coverage and length, this book originated from lecture courses at the Ecole Poly technique. It is useful to re- mind non-French readers of the special place this institution occupies in our education system, as it has few features in common with institutes with a similar name in other parts of the world. In fact, its programme corresponds to the intermediate years at a university, while the level of the students is particularly high owing to their strict selection through entrance examina- tions. The courses put a stress on giving foundations with a balance between the various natural and mathematical sciences, without neglecting general cultural aspects; specialization and technological instruction follow after the students have left the Ecole. The students form a very mixed population, not yet having made their choice of career. Many of them become high-level engineers, covering all branches of industry, some devote themselves to pure or applied research, others become managers or civil servants, and one can find former students of the Ecole amongst generals, the clergy, teachers, and even artists and Presidents of France. Several features of the present volume, and in particular its contents, correspond to this variety and to the needs of such an audience. Statistical physics, in the broadest meaning of the term, with its many related disci- plines, is an essential element of modern scientific culture.