This book, "Substitution Dynamical Systems – Spectral Analysis," by Martine Queffélec, focuses on the spectral analysis of substitution dynamical systems. The author aims to provide a comprehensive and unified description of the spectrum of these systems, particularly those arising from substitutions of constant length. The book covers various aspects of the subject, including combinatorics, ergodic theory, and harmonic analysis of measures. The introduction highlights the historical development of substitution dynamical systems, starting with the construction of the Morse sequence by Thue in 1906. The book discusses different types of sequences and dynamical systems derived from substitutions, such as substitution sequences, generalized Morse sequences, and q-multiplicative sequences. It emphasizes the spectral properties of these systems, including strict ergodicity, entropy, and mixing properties. The text is structured into chapters that cover the algebraic and spectral theory of unitary operators, spectral theory of dynamical systems, and specific applications to sequences and substitutions. Key topics include generalized Riesz products, correlation measures, and the spectral decomposition theorem. The book also addresses the spectral properties of specific sequences like the Morse and Rudin-Shapiro sequences, and discusses the spectral multiplicity of general automata. The author acknowledges the contributions of various mathematicians and specialists who have influenced the field, and provides a detailed bibliography and index to support further study. The book is designed to be accessible to non-specialists, with detailed explanations of key concepts and examples.This book, "Substitution Dynamical Systems – Spectral Analysis," by Martine Queffélec, focuses on the spectral analysis of substitution dynamical systems. The author aims to provide a comprehensive and unified description of the spectrum of these systems, particularly those arising from substitutions of constant length. The book covers various aspects of the subject, including combinatorics, ergodic theory, and harmonic analysis of measures. The introduction highlights the historical development of substitution dynamical systems, starting with the construction of the Morse sequence by Thue in 1906. The book discusses different types of sequences and dynamical systems derived from substitutions, such as substitution sequences, generalized Morse sequences, and q-multiplicative sequences. It emphasizes the spectral properties of these systems, including strict ergodicity, entropy, and mixing properties. The text is structured into chapters that cover the algebraic and spectral theory of unitary operators, spectral theory of dynamical systems, and specific applications to sequences and substitutions. Key topics include generalized Riesz products, correlation measures, and the spectral decomposition theorem. The book also addresses the spectral properties of specific sequences like the Morse and Rudin-Shapiro sequences, and discusses the spectral multiplicity of general automata. The author acknowledges the contributions of various mathematicians and specialists who have influenced the field, and provides a detailed bibliography and index to support further study. The book is designed to be accessible to non-specialists, with detailed explanations of key concepts and examples.