This book provides a comprehensive and unified analysis of the spectrum of dynamical systems arising from substitutions of constant length. It explores the connections between combinatorics, ergodic theory, and harmonic analysis of measures. The study begins with the historical development of substitution systems, starting with Thue's 1906 sequence and Morse's rediscovery in 1921. The book presents a detailed approach to analyzing the spectrum of substitution dynamical systems, focusing on the spectrum of the unitary operator adjoint to the system. It discusses various types of sequences, including substitution sequences, generalized Morse sequences, and q-multiplicative sequences. The text covers ergodic and topological properties of substitution dynamical systems, including strict ergodicity, entropy, and mixing properties. It also addresses the spectral analysis of the continuous part of the spectrum, highlighting the importance of maximal spectral type and spectral multiplicity. The book includes detailed discussions on Riesz products, correlation measures, and matrices of measures, with examples such as the Morse sequence and Rudin-Shapiro sequence. It also explores the spectral properties of substitution systems with non-constant length and presents recent results on eigenvalues and spectral multiplicity. The text is self-contained, accessible to non-specialists, and includes a detailed treatment of key concepts in spectral theory and dynamical systems. The book concludes with a discussion of the spectral multiplicity of general automata and an appendix on compact automata. The content is organized into chapters covering various aspects of substitution dynamical systems, including algebraic structures, spectral theory, and applications.This book provides a comprehensive and unified analysis of the spectrum of dynamical systems arising from substitutions of constant length. It explores the connections between combinatorics, ergodic theory, and harmonic analysis of measures. The study begins with the historical development of substitution systems, starting with Thue's 1906 sequence and Morse's rediscovery in 1921. The book presents a detailed approach to analyzing the spectrum of substitution dynamical systems, focusing on the spectrum of the unitary operator adjoint to the system. It discusses various types of sequences, including substitution sequences, generalized Morse sequences, and q-multiplicative sequences. The text covers ergodic and topological properties of substitution dynamical systems, including strict ergodicity, entropy, and mixing properties. It also addresses the spectral analysis of the continuous part of the spectrum, highlighting the importance of maximal spectral type and spectral multiplicity. The book includes detailed discussions on Riesz products, correlation measures, and matrices of measures, with examples such as the Morse sequence and Rudin-Shapiro sequence. It also explores the spectral properties of substitution systems with non-constant length and presents recent results on eigenvalues and spectral multiplicity. The text is self-contained, accessible to non-specialists, and includes a detailed treatment of key concepts in spectral theory and dynamical systems. The book concludes with a discussion of the spectral multiplicity of general automata and an appendix on compact automata. The content is organized into chapters covering various aspects of substitution dynamical systems, including algebraic structures, spectral theory, and applications.