The axial bar is the simplest case of a theory of deformable solids. It has all the features of every deformable solids problem—what we call the three legs of the mechanics stool (equilibrium, kinematics, and constitution). As such, it is a good framework for introducing the basic ideas of the mechanics of deformable solids. While the axial bar has practical import on its own, the main objective of this chapter is to explore how the essential components of the theory fit together in a mathematical context that involves only a single scalar internal force function and a single scalar displacement function. In essence, this chapter is a roadmap to the rest of the book.