ABSTRACT This contribution introduces the basic concepts of Fracture Mechanics in linear elastic materials. A brief review of the history of Fracture Mechanics is given in the first section of the paper. Then we present the asymptotic behavior of the mechanical fields near the crack fronts. Basic fracture modes and corresponding stress intensity factors are defined. An energy analysis of crack propagation is performed, the energy released rate and the path-independent J integral are introduced. We finally present fracture propagation criteria, for simple or mixed mode loadings.