Engineers of all types contribute to science and technology for the benefit of mankind. Mathematical models, engineering experiments, and numerical simulations constitute the three main pillars of scientific activity. The most challenging task for engineers is to identify a suitable mathematical model of the system's behavior. This chapter is devoted to a review of preliminaries from engineering mechanics. The review includes: vectors and tensors, the definitions of the Green–Lagrange strain tensor, infinitesimal strain tensor, measures of stress, equations of elasticity, and stress–strain relations for plane stress problems, an introduction to functionally graded materials, and an introduction to the modified couple stress concept. Functionally graded materials are characterized by the variation in composition of two or more materials gradually over surface or volume, resulting in a composite material that has desired properties.