The purpose of the School, the content of which is reflected in this book, is to bring together experiences and knowledge of those acousticians who are particularly sensible to materials and their properties, specifically to those materials that may be called inhomo geneous. The two things together: acoustics and inhomogeneity, define factually a dimension less parameter, AI a, which is the ratio between the sound wavelength and the spatial length of the material where its physical characteristics notably change. An implicit defmition is, therefore, at hand for an inhomogeneous medium, which has the characteristic of a condi tioned definition and sets a looser constraint to the otherwise strict statement of invariance under translations. Composite, biologicai, porous, stratified materials are in the list of inhomogeneous materials, whose technological or structural interest has grown greatly in recent times. Ul trasonic waves offer a means for their investigation, which is valuable for it can be non destructive, continuous in time, spatially localized, dependent on the size of inhomoge neities."