The lecture provides an introduction to the fundamentals and engineering applications of elasticity theory. Central concepts - such as stresses, strains and constitutive law - are introduced in three-dimensional space, with constitutive law initially limited to linear elasticity theory. Subsequently, analytical solution methods for special inhomogeneous two- and three-dimensional boundary value problems are developed. Furthermore, one-dimensional nonlinear rheological models for viscoelastic and elastoplastic material behavior are discussed. This is followed by the treatment of fundamentals of the finite element method, with a restriction to the one-dimensional case. The module is the basis for numerous other modules in the compulsory and elective areas.