The description of the book already gives a very good overview:
Summary from the cover of the book: “The book is an introduction, for both graduate students and newcomers to the field of the modern theory of mesoscopic complex systems, time series, hypergraphs and graphs, scaled random walks, and modern information theory. As these are applied for the exploration and characterization of complex systems. Our self-consistent review provides the necessary basis for consistency. We discuss a number of applications such diverse as urban structures and musical compositions.”
In the Preface the author wrote: “In particular, we discuss
– how local and global properties of complex systems are related to each other (i.e., geometry);
– how uncertainty in the environmental conditions and immediate transitions are related to uncertainty of the infinitely long paths (or sequences of transformations) in complex systems (i.e., predictability);
– which part of information is lost in transitions and which part is stored and have repercussions in the future evolution of the complex system (i.e., selectivity).”
The book is very large structured in 8 chapters and References – Index:
Chapter 1. Perplexity of Complexity – with 19 subchapters
Chapter 2. Preliminaries: Permutations, Partitions, Probabilities and Information – with 12 subchapters
Chapter 3. Theory of Extreme Events – with 15 subchapters
Chapter 4. Statistical Basis of Inequality and Discounting the Future and Inequality – with 8 subchapters
Chapter 5. Elements of Graph Theory: Adjacency, Walks and Entropies – with 17 subchapters
Chapter 6. Exploring Graph Structures by Random Walks – with 17 subchapters
Chapter 7. We Shape Our Buildings; Thereafter They Shape Us – with 11 subchapters
Chapter 8. Complexity of Musical Harmony – with 8 subchapters
The book contains 246 references on this topic and the Index contains 225 items.
Some material in Section 8 is reprinted from the previous paper by the author and J. R. Dawin [Markov chain analysis of musical dice games. World Scientific, 204–229 (2012; Zbl 1356.00008)], and [arXiv:1004.4198].
Here the pictures are in a better quality: colored and not only grew scaled, cp. e.g. Fig. 8.47 on p. 249 in the book and Figure 9 in [arXiv:1004.4198].
The book can be recommended to all readers, who are interested in this field.