  Recent discoveries have demonstrated that matter can be distinguished on the
basis of topological considerations, giving rise to the concept of topological
phase. Introduced originally in condensed matter physics, the physics of
topological phase can also be fruitfully applied to plasmas. Here, the theory
of topological phase is introduced, including a discussion of Berry phase,
Berry connection, Berry curvature, and Chern number. One of the clear physical
manifestations of topological phase is the bulk-boundary correspondence, the
existence of localized unidirectional modes at the interface between
topologically distinct phases. These concepts are illustrated through examples,
including the simple magnetized cold plasma. An outlook is provided for future
theoretical developments and possible applications.
