This book is based on the modern conceptual understanding of crystal fields. It 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. This comprehensive volume provides readers with clear instructions and a set of computer programs for the phenomenological analysis of energy spectra of magnetic ions in solids. Readers are shown how to employ a hierarchy of parametrized models to extract as much information as possible from observed lanthanide and actinide spectra. All computer programs included in the volume are freely available on the Internet. It will be of particular interest to graduate students and researchers working in the development of opto-electronic systems and magnetic materials.