This book reviews the theory of extreme values for random sequences and processes, written by M.R. Leadbetter, G. Lindgren, and H. Rootzen. Since the publication of E.J. Gumbel's "Statistics of Extremes" in 1958, the theory of extreme values has evolved from focusing on independent, identically distributed random variables to encompassing dependent sequences and continuous parameter stochastic processes. The authors present a unified general theory that includes classical lines, covering one-dimensional stochastic sequences and processes. The book is divided into four parts. Part I discusses the classical extreme value theory for independent, identically distributed random variables and introduces the main ideas for extending the theory. Part II focuses on stationary sequences, particularly dependent sequences where the asymptotic distribution of extreme values is similar to that of independent sequences. Part III extends the theory to continuous parameter stationary stochastic processes, emphasizing differentiable and non-differentiable normal processes. Part IV discusses applications of extreme value theory, aiming to demonstrate thoughtful case studies based on physical principles rather than just illustrating classical distributions. An appendix provides an introduction to point processes, including convergence concepts. The book is written clearly and is recommended as a textbook or reference for students and researchers interested in extreme value theory. It covers a significant portion of recent published and unpublished papers and is a valuable contribution to the literature.This book reviews the theory of extreme values for random sequences and processes, written by M.R. Leadbetter, G. Lindgren, and H. Rootzen. Since the publication of E.J. Gumbel's "Statistics of Extremes" in 1958, the theory of extreme values has evolved from focusing on independent, identically distributed random variables to encompassing dependent sequences and continuous parameter stochastic processes. The authors present a unified general theory that includes classical lines, covering one-dimensional stochastic sequences and processes. The book is divided into four parts. Part I discusses the classical extreme value theory for independent, identically distributed random variables and introduces the main ideas for extending the theory. Part II focuses on stationary sequences, particularly dependent sequences where the asymptotic distribution of extreme values is similar to that of independent sequences. Part III extends the theory to continuous parameter stationary stochastic processes, emphasizing differentiable and non-differentiable normal processes. Part IV discusses applications of extreme value theory, aiming to demonstrate thoughtful case studies based on physical principles rather than just illustrating classical distributions. An appendix provides an introduction to point processes, including convergence concepts. The book is written clearly and is recommended as a textbook or reference for students and researchers interested in extreme value theory. It covers a significant portion of recent published and unpublished papers and is a valuable contribution to the literature.