MHD waves in homogeneous and continuously stratified atmospheres

The basic equations, concepts, and modes of linear, ideal, MHD waves -- slow, Alfv\'en and fast -- are set out and generalised to gravitationally-stratified atmospheres. Particular attention is devoted to mode conversion, wherein the local behavior of a global wave changes from one mode to another in passing through particular atmospheric layers. Exact solutions are explored where available. Eikonal methods -- WKBJ and ray theory -- are described. Although our emphasis is on the theoretical underpinning of the subject, the solar atmospheric heating implications of fast/slow and fast/Alfv\'en conversions are discussed in detail.