The authors of this book, part of the “SpringerBriefs in Mathematics” series, have extensive backgrounds in the area covered.

The book, organized into seven chapters, starts with a comprehensive preface, which includes historical background such as Brualdi et al.’s “concept of a metric on a vector space determined by a partial order over a finite set, a poset.” The preface claims that this book is “the first title to give a systematic approach [to] poset metrics and code.” As a skeptic, I wanted to check this claim, so over a two-week period I searched for the contrary; I am now convinced that this book is the first comprehensive coverage of the area. It should be the starting point for anyone interested in poset metrics and codes. However, a word of caution: a reasonable knowledge of coding theory, vector spaces, some combinatorics, and general mathematics is needed to get the most out of this work. The book reads like something in between a research monograph and an advanced text on the topic of poset metrics and codes. As a practitioner of coding theory in engineering, I found the book useful for general awareness but not for practical use.

Each chapter starts with a nice introduction and ends with concluding remarks as “Chapter Notes.” These notes are useful for readers who want a general idea without digging into the details covered in the chapter. Although the preface states that there is an epilogue after chapter 7, I could not find one.

In conclusion, for a mathematically mature audience, this advanced monograph compiles and presents poset metrics in a systematic way. Instead of reading many papers, one can study the area all in one place. The book can be useful to mathematically oriented electrical engineering and computer science researchers.