This book is based on the modern conceptual understanding of crystal fields. It provides readers with clear instructions and a set of computer programs for the phenomenological analysis of energy spectra of magnetic ions in solids. The text clarifies several issues that have historically produced confusion in this area, particularly the effects of covalency and ligand polarization on the energy spectra of magnetic ions. Readers are shown how to employ a hierarchy of parametrized models to extract as much information as possible from observed lanthanide and actinide spectra. This is the first book in the area of crystal field theory which describes all of the available phenomenological models, together with the conceptual and computational tools necessary for their use. It will be of particular interest to graduate students and researchers working in the development of opto-electronic systems and magnetic materials.