This two-part book presents modern ideas and original research on the theory of main cracks that can propagate in solid deformable bodies, leading to partial or complete destruction. The content of the book covers a wide range of issues of the behavior of bodies with cracks - from criteria for crack propagation to solving a number of complex problems of fracture mechanics. Limit and pre-limit equilibrium states under single, multiple, thermal and dynamic loads in elastic, viscoelastic, elastoplastic and piezoelectric bodies with cracks are considered. Methods of experimental determination of crack resistance characteristics of materials are described.