In this volume we aim to introduce recent progress in the study of aperiodic materials, which include icosahedral clusters, amorphous metals, quasicrys tals, glasses, and liquids. Quasicrystals, discovered in 1984, correspond to a kind of revolution in our understanding of crystallography, wherein the five-fold rotational symmetry was prohibited in long-range ordered systems. Various interesting physicochemical properties of these materials strongly depend on structural inhomogeneity at the microscopic level, and the small angle X-ray scattering method is widely used to analyze such...