The chapter introduces the theory of molecular excitons, a significant area of research in solid-state physics. The author, A. S. Davydov, a renowned physicist from Kiev State University, provides an overview of the development of the theory, highlighting its importance in understanding the optical properties of solids. The book covers fundamental concepts, including the phenomenological theory of electromagnetic waves in dielectric media, the elementary theory of excitons, and the second-quantization representation of exciton states. It also discusses the interaction of excitons with phonons and photons, and the dielectric constant of molecular crystals with lattice vibrations. The chapter emphasizes the progress in experimental and theoretical research on exciton states, noting that while significant advancements have been made, monographs have not fully reflected these developments. The author aims to provide a comprehensive and up-to-date treatment of the theory, reflecting his own contributions to the field.The chapter introduces the theory of molecular excitons, a significant area of research in solid-state physics. The author, A. S. Davydov, a renowned physicist from Kiev State University, provides an overview of the development of the theory, highlighting its importance in understanding the optical properties of solids. The book covers fundamental concepts, including the phenomenological theory of electromagnetic waves in dielectric media, the elementary theory of excitons, and the second-quantization representation of exciton states. It also discusses the interaction of excitons with phonons and photons, and the dielectric constant of molecular crystals with lattice vibrations. The chapter emphasizes the progress in experimental and theoretical research on exciton states, noting that while significant advancements have been made, monographs have not fully reflected these developments. The author aims to provide a comprehensive and up-to-date treatment of the theory, reflecting his own contributions to the field.