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Materials containing atoms with an open f shell have special electronic and crystalline properties that are controlled by the localized or extended character of the f states.§This book aims at giving a theoretical discussion of the various spectroscopic methods that shed light on the character of the f states and on the connection between their localisation and those properties.§Part 1 of the book will cover the behaviour of the f states in atoms and solids and include discussion of the electronic properties of lanthanides and actinides in connection with these f states.§§Part 2 will describe the various spectroscopic methods used to establish the distribution and energies of the electronic states. Examples will deal with the determination of the f state distributions. Among the methods discussed are optical spectroscopies (involving valence levels) and high-energy spectroscopies (involving core levels).§Part 3 concentrates on the theoretical treatment of the electronic transitions involving f states and simulation of their spectra and includes comparison with experimental data.§Finally, Part 4 discusses the localized or extended behaviour of the f states in lanthanides and actinides. There is also comparison (analogies and differences) between the 4f and 5f electrons.