The book "Solitons in Molecular Systems" by A. S. Davydov, translated by Dr. Eugene S. Kryachko, is part of the "Mathematics and Its Applications" series published by Springer-Science+Business Media. The book covers the theory and applications of solitons in molecular systems, focusing on their collective excitations, dynamical properties, and interactions with external fields. It explores solitons in one-dimensional molecular systems, including their formation, evolution, and behavior under various conditions such as friction and external inhomogeneous fields. The book also discusses solitons in molecular systems with nonlinear intermolecular interactions, super-sound acoustic solitons, electron transfer by solitons, and space-periodic excitations in nonlinear systems. Additionally, it delves into the nonlinear sine-Gordon equation, long waves in nonlinear media, and solitons in three-dimensional ionic crystals. The author emphasizes the interdisciplinary nature of soliton research, highlighting its applications in physics, chemistry, biology, and mathematics. The book is intended for researchers and students interested in the theoretical and practical aspects of solitons in molecular systems.The book "Solitons in Molecular Systems" by A. S. Davydov, translated by Dr. Eugene S. Kryachko, is part of the "Mathematics and Its Applications" series published by Springer-Science+Business Media. The book covers the theory and applications of solitons in molecular systems, focusing on their collective excitations, dynamical properties, and interactions with external fields. It explores solitons in one-dimensional molecular systems, including their formation, evolution, and behavior under various conditions such as friction and external inhomogeneous fields. The book also discusses solitons in molecular systems with nonlinear intermolecular interactions, super-sound acoustic solitons, electron transfer by solitons, and space-periodic excitations in nonlinear systems. Additionally, it delves into the nonlinear sine-Gordon equation, long waves in nonlinear media, and solitons in three-dimensional ionic crystals. The author emphasizes the interdisciplinary nature of soliton research, highlighting its applications in physics, chemistry, biology, and mathematics. The book is intended for researchers and students interested in the theoretical and practical aspects of solitons in molecular systems.