Characterization of Surface Roughness.- The Kirchhoff and Related Approximations.- Scattering and the Spatial Frequency Representation.- Rayleigh Hypothesis.- Small-Amplitude Perturbation Theory for One-Dimensionally Rough Surfaces.- Small-Amplitude Perturbation Theory for Two-Dimensional Surfaces.- Computer Simulations of Rough Surface Scattering.- Overview of Rough Surface Scattering.- Experimental Studies of Scattering from Weakly Rough Metal Surfaces.- Measuring Interfacial Roughness by Polarized Optical Scattering.- Scattering of Electromagnetic Waves from Nanostructured, Self-Affine Fractal Surfaces: Near-Field Enhancements.- Light Scattering by Particles on Substrates. Theory and Experiments.- Multiple Scattering of Waves by Random Distribution of Particles for Applications in Light Scattering by Metal Nanoparticles.- Multiple-Scattering Effects in Angular Intensity Correlation Functions.- Speckle Pattern in the Near Field.- Inverse Problems in Optical Scattering.- The Design of Randomly Rough Surfaces That Scatter Waves in a Specified Manner.

All real surfaces, both those occurring naturally, and those fabricated artificially and with great care, are rough to some degree. It is therefore of interest, and often of importance, to know the extent to which this roughness affects physical p- cesses occurring at a surface. A particularly interesting class of physical processes occurring at a rough surface is the scattering of electromagnetic waves from it, or their transmission through it. In this case the degree of the surface roughness is referred to the wavelength of the waves incident on it. The study of the scattering of electromagnetic waves from rough surfaces has been actively carried out for more than a century now, since Rayleigh's inves- gations of the scattering of a monochromatic plane wave incident normally on a 1 sinusoidal interface between two different media. The first theoretical treatment of the scattering of an electromagnetic wave from a randomly rough surface was due to Mandel'shtam/ in the context of the scattering of light from a liquid s- face. In these pioneering studies the angular dependence of the intensity of the scattered field was calculated by perturbation theory as an expansion in powers of the surface profile function though the first nonzero term, a single scattering approximation.