This book contains selected papers of Jürg Fröhlich, one of the most outstanding mathematical physicists of our time, on the subject of statistical mechanics. In an extensive introduction, Jürg Fröhlich sets his results into a wider context and gives precious information on the genesis of his work from both a historical and a methodological perspective. It is not only an overview of current and future research directions in statistical mechanics, but also relates this subject with other branches of contemporary physics and mathematics. All papers in this collection bear Jürg Fröhlich’s signature in terms of a delicate balance between mathematical rigor and physical significance. They cover thirty years of his work on statistical physics, ranging from the most basic foundational questions in atomism and thermodynamics via the description of phase transitions and critical phenomena up to disordered systems and the study of many-body systems in condensed matter physics, including the quantum Hall effect. The wide range of topics covered in this compendium reflects the breadth of Jürg Fröhlich’s interests, and the last chapters reveal an outlook towards some of his more recent research areas.