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This book is conceived as a monograph, and represents an up-to-date collection of information concerning the use of the method of X-ray photoelectron spec- troscopy in the study of the electron structure of crystals, as well as a personal interpretation of the subject by the authors. In a natural way, the book starts in Chapter 1 with a recapitulation of the fundamentals of the method, basic relations, principles of operation, and a com- parative presentation of the characteristics and performances of the most com- monly used ESCA instruments (from the classical ones-Varian, McPherson, Hewlett Packard, and IEEE-up to the latest model developed by Professor Siegbahn in Uppsala), and continues with a discussion of some of the difficult problems the experimentalist must face such as calibration of spectra, prepara- tion of samples, and evaluation of the escape depth of electrons. The second chapter is devoted to the theory of photoemission from crystal- line solids. A discussion of the methods of Hartree-Fock and Hartree-Fock- Slater for the calculation of bonding energy levels in multielectronic systems is presented, and the necessity of including in the theory both relativistic and relaxation effects is argued.