Background on Continuum Damage Mechanics -- Numerical Analysis of Damage -- Ductile Failures -- Low Cycle Fatigue -- Creep, Creep-Fatigue, and Dynamic Failures -- High Cycle Fatigue -- Failure of Brittle and Quasi-Brittle Materials.Engineering Damage Mechanics is deliberately oriented toward applications of Continuum Damage Mechanics to failures of mechanical and civil engineering components in ductile, creep, fatigue and brittle conditions depending upon the thermomechanical loading and the materials: metals and alloys, polymers, elastomers, composites, concretes. Nevertheless, to help engineers, researchers, beginners or not, the first two chapters are devoted to the main concepts of damage mechanics and to the associated computational tools.