There are several books out there that provide a theoretical discussion of the theory of extreme values. However, the treatment of applications is often neglected. This book sets out to deal with both issues: the statistical analysis and the applications of extreme values. Modeling, statistical inference, and analysis are all done with exceptional attention to the details.

The first part of the book deals with the theoretical aspect. It can be divided into three parts: modeling and data analysis, statistical inference, and multivariate statistical analysis. The concepts are presented in a narrative style rather than a strict theorem-proof presentation. The author states the results and provides interpretation and discussion. Illustrations are presented throughout the text for further clarification and understanding.

The mathematical exposition is at medium difficulty, i.e. reader with appropriate background in upper undergraduate or graduate mathematical statistics and probability should be well prepared to grasp the text efficiently. The examples further enhance the text. They are presented very well, explaining the data, the problem and the solution. Examples vary from smaller ones that contribute to the current theory being presented and larger ones that encompass a whole section.

The second part of the book deals with practical applications in hydrology, environmental science, finance, insurance, material and life sciences. The level of detail varies. For example, the examples in finance start out by explaining the problem in great detail along with the illustration of some very elementary concepts such as autocorrelation, volatility of returns, and parameter estimation. Later on the concept of VaR is given theoretically and results are presented based on an external study.

Given that the book presents itself as applied, the section on applications should be presented in much greater perspective. What is given is most likely already known to most serious practitioners. It might be enough, however, for students starting to explore the field.

This book would be very suitable for a practical applied course (more like a workshop or open seminar) at either the graduate or upper undergraduate level. Such an approach would allow readers to enhance the applied side of the book. Practitioners should find this book useful to learn the theory and concepts.

Ita Cirovic Donev is a PhD candidate at the University of Zagreb. She hold a Masters degree in statistics from Rice University. Her main research areas are in mathematical finance; more precisely, statistical mehods of credit and market risk. Apart from the academic work she does consulting work for financial institutions.