||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 Encyclopedia 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 (Ch.I,II,III,VIII) is still based on three articles written as entries for the —it Encicopledia della Fisica (namely: "Mec-canica Statistic^, "Teoria degli Insiemf and "Moto Browniano") which make up about 29% of the present book and, furthermore, it still contains (with little editing and updating) my old review article on phase transitions (Ch.VI, 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).
The aim was to provide an analysis, intentionally as nontechnical as I was able to make it, of many fundamental questions of Statistical Mechanics, about two centuries after its birth. Only in a very few places have I entered into really technical details, mainly on subjects that I should know rather well or that I consider particularly important (the convergence of the Kirkwood-Salsburg equations, the existence of the thermodynamic limit, the exact soltution of the Ising model, and in part the exact solution of the six vertex models). The points of view expressed here were presented in innumerable lectures and talks mostly to my students in Roma during the last 25 years. They are not always "mainstream views"; but I am confident that they are not too far from the conventionally accepted "truth" and I do not consider it appropriate to list the differences from other treatments. I shall consider this book a success if it prompts comments (even if dictated by strong disagreement or dissatisfaction) on the (few) points that might be controversial. This would mean that the work has attained the goal of being noticed and of being worthy of criticism.
I hope that this work might be useful to students by bringing to their attention problems which, because of "concreteness necessities" (i.e. because such matters seem useless, or sometimes simply because of lack of time), are usually neglected even in graduate courses.