The first thing to say about this book is that the title is misleading as it is not an encyclopedia – it is a series of definitions thematically grouped into chapters and parts, starting with more general ideas relating to distance and then getting progressively more specialised. The description of it as a coffee table book would also be incorrect as it isn't large format and the only pictures it contains are two small photographs of Fréchet and Hausdorff in the acknowledgements. It does, though, contain an interesting collection of articles; mainly related to distances used in maths, but also covers other subject areas. As well as discussing the theory of distances in different geometries, topologies, spaces, metrics, graphs and transforms, it also covers “real‐world” distances ranging from 1.6×10−35m (the Planck length) to 4.3×1026m (the estimated size of the observable Universe).
Its main audience is researchers who are interested in an aspect of distance and its measurement. It does require quite a high level of maths knowledge of the reader: the first chapter starts well above the mathematical knowledge of most general readers (I would estimate that much of it requires a maths‐related degree) and I doubt that many of the general public would read beyond the first page, although the later chapters are more understandable to a non‐specialist. And the majority of entries include multiple formulae, which looks quite daunting, especially as they are generally not explained.
The idea of this book is to combine in one place distances and distance metrics used in one specific area to be available/explained for those who are working on a similar idea, but in a different research area. Distance is a fundamental idea in so many subjects and this book is aiming to combine different aspects of distance from different subjects in one place. The descriptions of each entry do not try to give value to different metrics and so the reader is left to judge which distance function is best for their specific situation.
The range of subject areas covered within the book, from cosmology to economics, as well as maths, shows how key distance is to different subject areas. The first part of the book is an introduction, explaining the general ideas of distance, and then part two covers geometry, part three classical maths and part four applied maths. Part five covers computing, part six other sciences and then part seven is called Real‐World Distances and covers more general distances that are of interest to a non‐specialist. Entries cover ideas like the monkey saddle metric, flower shop metric, airlift distance, web hyperlink‐quasi‐metric and the phonetic word distance.
The book includes a comprehensive index but the references are limited, although the preface explains the authors' rationale for inclusion of references. Each definition clearly identifies where it is building on other definitions in the book so the reader can refer to those entries as well.
Overall, this is a specialist reference book, and as such is not designed to be read from cover‐to‐cover. It does require a high level of knowledge of the subject, especially maths, before reading and so is not a suitable introduction to the topic. For those who are already knowledgeable in this subject then it would be an interesting review and could introduce other aspects of distance with which they might be unfamiliar.
