This is a comprehensive guide to a fascinating mathematical and computational perspective on real-world social phenomena: multilayer networks. It is authored by researchers who are experts in data science, social network modeling, mining, and machine learning. The book attracts the reader’s interest from the first lines: it opens with an example of a Twitter post regarding Osama Bin Laden’s death, which spread rapidly to all types of media and reached millions of people. The example aptly highlights the multidimensional and complex nature of today’s society, and serves as an excellent introduction to the philosophy behind the book; that is, our social experiences are not the result of a single network, but of multiple overlapping social and media networks that are interconnected in complex and usually invisible ways. The subsequent need for mathematical and computational theories, methods, and tools for moving from a traditional mono-dimensional to a multidimensional perspective of social networks is cleverly parallelized with a journey away from “Flatland,” a fictional world created by Edwin A. Abbot in his 1884 novel. The message is clear: traditional graph theory with simple graphs comprised of nodes and edges needs to be extended toward new directions and dimensions in order to be able to capture the multi-relational nature of social phenomena. The perspective of multiple layers is such a direction, and its utilization is fully justified by the challenging needs of the related research problems. Therefore, this is exactly the aim of the book: to review the advances of the multilayer social network methodologies as a consolidated guide to a continuously evolving research area. Moreover, the book aims to establish consistent terminology for the subject, which can also be used in generic multilayer networks, not only social ones.

The material is organized in four parts, each containing adequately self-contained chapters (in total, ten). However, some chapters are of special importance for the reader since they contain fundamental notions and terminology. In general, the text is easily readable; although the notions described are mathematical and abstract, the minimum level of mathematical formalism, the gradual presentation of notions, and the clarifying examples make the book accessible to a wide and interdisciplinary audience, one that does not necessarily require a strong mathematical background.

After an introductory chapter 1, Part 1 deals with models and measures of multilayer social networks. It contains two corresponding chapters. Chapter 2 presents the terminology and a general multilayer model, which includes special case models for multiple types of nodes, multiple types of relations, and multiple interdependent social networks. These special cases are presented historically and with respect to their application domains. The chapter also presents cases with data that are used as examples in the book. Chapter 3 presents the basic metrics of multilayer social networks (degree, neighborhood centrality, multidimensional distances, betweenness, transitivity, relevance, and layer correlation) as an extension of the traditional metrics used in network analysis.

Part 2 is devoted to mining multilayer networks. Chapter 4 deals with data collection and preprocessing. Various aspects of data collection, such as sampling and missing data, are discussed, along with methods aiming to simplify the complexity of multiple layers. Chapter 5 follows naturally the data preparation stage and presents the visualization methods that have been developed for a first optical investigation of possible patterns and correlations. Chapter 6 focuses on a social network subject, extensively studied in the literature: community detection. The chapter presents a thorough account of relevant existing methods for multilayer networks. The final chapter of this part (7) discusses other mining problems such as edge prediction, that is, the prediction of new relations expressed as links and the discovery of associations between ties in different layers.

Part 3 deals with dynamical processes of multilayer networks related to their evolution. Chapter 8 reviews the modeling of multiple layers’ co-evolution, starting from general formation properties and single-layer formation and continuing to multilayer formation. Another dynamical aspect of networks, the diffusion process, is treated in chapter 9. This chapter specifically discusses the peculiarities of the spread of information, opinions, and behavior in multilayer networks.

The last part (4), containing a single chapter (10), concludes the book. As the area is new and promising with lots of open problems, but also with its own research perspectives and challenges, this chapter discusses directions for future research in relation to the topics of the previous chapters.

Overall, the book provides a thorough introduction to multilayer social networks, followed by an extensive literature review. The intensive interest and the enthusiasm of the authors for this area are contagious and stimulate the readers to further explore multilayer networks as tools for their own research domains. Hence, the book is recommended to researchers, practitioners, and teachers who are eager to “escape from Flatland” and investigate new dimensions.