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ways in which the magnetic interaction between neutrons and magnetic moments can yield information on the magnetization densities of thin?lms and multilayers. I commend the organizers for having organized a group of expert lecturers to present this subject in a detailed but clear fashion, as the importance of the subject deserves. Argonne, IL S. K. Sinha Contents 1 The Interaction of X-Rays (and Neutrons) with Matter.............. 1 F. de Bergevin 1. 1 Introduction.............................................. 1 1. 2 Generalities and De?nitions................................ 2 1. 3 From the Scattering by an Object to the Propagation in a Medium. 14 1. 4 X-Rays.................................................. 26 1. 5 X-Rays: Anisotropic Scattering.............................. 47 1. A Appendix: the Born Approximation.......................... 54 References..................................................... 56 2 Statistical Aspects of Wave Scattering at Rough Surfaces............ 59 A. Sentenac and J. Daillant 2. 1 Introduction.............................................. 59 2. 2 Description of Randomly Rough Surfaces..................... 60 2. 3 Description of a Surface Scattering Experiment, Coherence Domains................................................. 67 2. 4 Statistical Formulation of the Diffraction Problem.............. 72 2. 5 Statistical Formulation of theScattered Intensity Under the Born Approximation........................................... 79 References..................................................... 84 3 Specular Re?ectivity from Smooth and Rough Surfaces............. 85 A. Gibaud and G. Vignaud 3. 1 The Re?ected Intensity from an Ideally Flat Surface............ 85 3. 2 X-Ray Re?ectivity in Strati?ed Media........................ 98 3. 3 From Dynamical to Kinematical Theory...................... 107 3. 4 In?uence of the Roughness on the Matrix Coef?cients.......... 111 3. A Appendix: The Treatment of Roughness in Specular Re?ectivity.. 113 3. B Appendix: Inversion of re?ectivity data.......................