Discussing the foundations of both classical and quantum statistical mechanics, this book aims to bridge a gap that exists between standard textbooks on the subject and more advanced books. It is devised for a one-semester course on statistical mechanics at the graduate level. Its prerequisite is therefore a more elementary course on the same subject. Emphasis is laid on the geometrical aspects of classical thermodynamics, on the foundational problems, and on selected applications, mainly to spin systems, the meaning of quantum statistics, phase transitions, critical phenomena and the renormalization group.