This research monograph is in some sense a sequel to the author's earlier one (Power System Stability, North Holland, New York 1981) which devoted cons- erable attention to Lyapunov stability theory, construction of Lyapunov fu- tions and vector Lyapunov functions as applied to power systems. This field of research has rapidly grown since 1981 and the more general concept of energy funct ion has found wide spread application in power systems. There have been advances in five distinct areas (i) Developing energy functions for structure preserving models which can incorporate non-linear load...