Beam theory is one of the most successful and widely used theories in engineering, having been refined and validated over the course of hundreds of years. It forms the basis of the subject of structural analysis and is at the heart of all commercial structural analysis codes today. This chapter shows how a simple kinematic hypothesis leads to the formulation of a complete mechanical theory governed by an ordinary differential equation that can be readily solved to generate practical results. From the theory, we can estimate the deflections of a beam under load and the stresses and strains that accrue in the process. In this chapter we establish the theory of beams, confining our attention to planar motion of beams. The developments of this chapter provide the theoretical foundation needed for most of the subsequent chapters.