Beams are slender structural elements which are employed to support transverse as well as axial loads. They are of very common use as columns, masts, lintels, joists etc, or as constitutive parts of supporting frames of buildings, cars, airplanes etc. They may be considered as the simplest structural element because of the relative simplicity of the equilibrium equations arising from a suitable condensation of the space variables into a single one, namely the abscissa along the beam length. However, the approximations used to represent in an appropriate manner the 3D solid as an equivalent 1D solid involve several subtleties, and several degrees of approximation can be proposed to refine the beam model when necessary. The object of this first of four chapters devoted to beams is to introduce the basic ideas of the elementary theory of beams. For the sake of simplicity at least, it is found convenient to adopt here a Newtonian instead of a variational approach. The latter will be adopted in the next chapters to establish more refined models than those presented here.