The evolution of the species has been studied for a long time; the scientist Carlos Linneo used a classification system in 1736 that has been modified with a phylogenetic one. As the authors mention in the preface, “The evolutionary history of a set of species is usually described by a rooted phylogenetic tree.” (This book contains a chapter that explains the basic concepts and definitions of phylogenetic trees for those, like me, who are not familiar with them.)

Nowadays, the relationship between biology and mathematics is stronger in this area; this book explains computational biology and mathematics in a way that is both rigorous and clear.

The book is divided into three parts. The first one is the introduction, which contains four chapters. Chapter 1 explains some basic concepts of the theory of graphs and systemics, and chapter 2 discusses aligning molecular sequences. Chapter 3 provides a more detailed introduction to the computation of phylogenetic trees. Chapter 4 serves as an introduction to phylogenetic networks and also as an overview for the material presented in the second and third parts of the book.

In the second part, the theoretical foundations for phylogenetic networks are developed. Chapter 5 studies splits and unrooted phylogenetic networks (splits provide the basis of unrooted phylogenetic trees and a large class of unrooted phylogenetic networks, namely, split networks). Over the last 20 years, the mathematical and computational aspects of such networks have been studied. Chapter 6 discusses clusters and phylogenetic networks. Their theory is still under development, and, as the authors point out, widely used methods for the computation of rooted phylogenetic networks have not emerged.

The third part of the book is devoted to a wide range of algorithms that have been developed for computing phylogenetic networks from biological data. For most of the methods, there is an application and references to papers that contain more details. The material is organized by type of input: chapter 7 with splits, chapter 8 with clusters, chapter 9 with sequences, chapter 10 with distances, chapter 11 with trees, and chapter 12 with triples or quartets. Chapter 13 addresses the problem of drawing phylogenetic networks. Finally, chapter 14 presents an overview of some existing software for computing phylogenetic networks.

This is an excellent book for readers who know the topic well and also for those who have some knowledge of the area.