Course covers 1) Introduction: the continuous medium; essential mathematics-scalars, vectors, tensors, indicial notations, transformations. 2) Basics: stress, strain and deformation; components, principal axes, tensors; 2D and 3D cases. 3) General principles: conservation of mass, continuity equation, momentum principal, motion and equilibrium, energy balance, constitutive equations: needs and axioms; ideal materials, elasticity, isotropy, plasticity, viscoelasticity and thermoelasticity. and 4) Applications: theory of elasticity, fluid mechanics.