This book is the end result of a long story that started with my involvement as Coordinator of the Statistical Mechanics section of the Italian Encyclopedia of Physics. An Italian edition collecting several papers that I wrote for the Encyclo­ pedia appeared in September 1995, with the permission of the Encyclopedia and the sponsorship of Consiglio Nazionale delle Ricerche (CNR-GNFM). The present work is not a translation of the Italian version but it overlaps with it: an important part of it (Chaps. 1-3, 8) is still based on three arti­ cles written as entries for the Enciclopedia della Fisica (namely: "Meccanica Statistica", "Teoria degli Insiemi" and "Moto Browniano") which make up about 29% of the present book and, furthermore, it still contains (with little editing and updating) myoId review article on phase transitions (Chap. 6, published in La Rivista del Nuovo Cimento). In translating the ideas into English, I introduced many revisions and changes of perspective as well as new material (while also suppressing some other material).