"This book offers a structured introduction to the subject, presenting its core concepts and main results. The book is self-contained and accessible to readers with a standard background in C*-algebras and von Neumann algebras, providing a solid foundation for engaging with the subject. This work serves as a valuable resource for experienced researchers, extending beyond the scope of standard textbooks, while also offering an excellent introduction to the topic." (Evgenios Kakariadis, zbMATH 1569.46001, 2026) "The book has ten chapters and five appendices. this book can serve as an introduction to the theory of KMS weights and KMS states, while it also leads to more advanced topics and presents some new results. It will be a useful resource for the research community working in this area and related topics." (Xin Li, Mathematical Reviews, October, 2025).