The rapid growth of the subject since the first edition ten years ago has made it necessary to rewrite the greater part of the book. Except for the introductory portion and the section on Mott scattering, the book has been completely revised. In Chap. 3, sections on polarization violating reflection symmetry, on resonance scattering, and on inelastic processes have been added. Chapter 4 has been rewritten, taking account of the numerous novel results obtained in exchange scattering. Chapter 5 includes the recent discoveries on photoelectron polarization produced by unpolarized radiation with unpolarized targets and on Auger-electron polarization. In Chap. 6, a further discussion of relativistic polarization phenomena has been added to the book. The immense growth of polarization studies with solids and surfaces required an extension and new presentation of Chap. 7. All but one section of Chap. 8 has been rewritten and a detailed treatment of polarization analysis has been included. Again, a nearly comprehensive treatment has been attempted. Even so, substantial selectivity among the wide range of available material has been essential in order to accomplish a compact presentation. The reference list, selected along the same lines as in the first edition, is meant to lead the reader through the literature giving a guide for finding further references. I want to express my indebtedness to a number of people whose help has been invaluable.