Fundamentally, a wave is simply a signal propagating through a medium (e.g., sound waves travel through the air via the vibration of air molecules). Surface gravity waves are waves propagating at the ocean–atmosphere interface driven by the large difference in density between water and air. Wind-driven seas and tsunamis are examples of surface gravity waves. The simplest description of such waves is through linear wave theory, which is also referred to as “Airy wave theory” after its formulation by the mathematician George Biddell Airy in the nineteenth century. This chapter will discuss the properties of linear waves, in addition to the assumptions and boundary conditions under which their mechanical behavior can be described.