Written for students and postgraduates who specialize in computer calculations, this book, volume I of a two-volume set, describes a new hierarchical model for dynamic nonlinear systems and discusses a set of new hierarchical principles. Modern hierarchical asymptotic methods are set forth, taking into account specific features of electrodynamic problems, and the phenomenon of hierarchy in electrodynamics is discussed. A set of hierarchical asymptotic calculative methods of two types is discussed in detail. Kulish is affiliated with the National Aviation University, Ukraine