Engineering Damage Mechanics is deliberately oriented toward applications of Continuous 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.