This book provides an introduction to the classical, quantum, and symmetry aspects of multipole theory, demonstrating the successes of the theory and also its unphysical aspects. It presents a transformation theory which removes these unphysical properties. The book will be of interest tophysics students wishing to advance their knowledge of multipole theory, and also a useful reference work for molecular and optical physicists, theoretical chemists working on multipole effects, solid state physicists studying the effects of electromagnetic fields on condensed matter, engineers andapplied mathematicians with interests in anisotropic materials. An interesting recent development has been the increasing use of computer calculations in applications of multipole theory. The book will assist computational physicists and chemists wishing to work in this area to acquire thenecessary background in multipole theory.