The chapter introduces the field of continuum damage mechanics, a rapidly developing branch of fracture mechanics. It emphasizes the importance of understanding damage phenomena in modern engineering materials, which can decrease strength due to microstructural changes under unfavorable mechanical and environmental conditions. The book aims to provide a systematic description of the basic aspects of damage mechanics and its applications. The author, L.M. Kachanov, acknowledges the complexity of theoretical descriptions and the scarcity of experimental data, particularly under multiaxial stress and non-proportional loading. The book focuses on practical engineering problems and avoids excessive mathematical formalism. The content covers various topics, including types of damage, damage variables, isotropic damage, kinetic equations, elastic bodies with damage, creep conditions, and fracture under uniaxial and multiaxial stress. It also discusses crack growth under creep conditions, damage models for ductile fracture, and fatigue damage. The book is likely the first comprehensive treatment of the subject and includes references, notations, and an index.The chapter introduces the field of continuum damage mechanics, a rapidly developing branch of fracture mechanics. It emphasizes the importance of understanding damage phenomena in modern engineering materials, which can decrease strength due to microstructural changes under unfavorable mechanical and environmental conditions. The book aims to provide a systematic description of the basic aspects of damage mechanics and its applications. The author, L.M. Kachanov, acknowledges the complexity of theoretical descriptions and the scarcity of experimental data, particularly under multiaxial stress and non-proportional loading. The book focuses on practical engineering problems and avoids excessive mathematical formalism. The content covers various topics, including types of damage, damage variables, isotropic damage, kinetic equations, elastic bodies with damage, creep conditions, and fracture under uniaxial and multiaxial stress. It also discusses crack growth under creep conditions, damage models for ductile fracture, and fatigue damage. The book is likely the first comprehensive treatment of the subject and includes references, notations, and an index.