The first chapter introduces the major concept of composite material, i.e., the combination of different components, to obtain in total much better properties than a single component for itself. The focus is many times on fiber-reinforced composites where a single layer has unidirectionally aligned reinforcing fibers. The basic equations of continuum mechanics to model such two-dimensional structures are introduced. A common approach is to avoid to solve the coupled system of differential equations. This is done by the so-called classical laminate theory for two-dimensional orthotropic composite materials. To facilitate the understanding, the idea of a simplified classical laminate theory is outlined. This reduced approach is based on one-dimensional bar/beam elements at which each single layer reveals isotropic properties.