'This remarkable near-encyclopaedic volume will become a classic text. Barry Simon's vision and knowledge are evident on every page, and the result is a must-have for experts and students alike. The material proceeds from the classical to the ultra-modern, including recent probabilistic methodology and a fascinating list of open problems.' Geoffrey Grimmett, University of Cambridge

'My old joke was that to study or research phase transitions in lattice models, install Barry Simon in your office to answer all questions. This book obviates the need for a live Barry, takes up less room and is not subject to AI hallucinations – Highly Recommended.' Chuck Newman, Courant Institute of Mathematical Sciences

'This volume on the theory of Lattice Gases covers most of the recent developments of statistical mechanics. Here, the scholar finds what the modern trends are, and what open problems one might work on. Together with Simon's previous book on Lattice Gases, it is an indispensable encyclopedia both for students and scientists interested in rigorous mathematical physics.' Senya Shlosman, Skolkovo Institute of Science and Technology