The book puts forward a novel and unique approach to describing amorphous solids, culminating in a theory of amorphousness that is equally well-founded as the theory of crystallography. A classification of amorphous materials into inorganic glasses, organic glasses, glassy metallic alloys and thin films sets the scene for the development of the model of ideal amorphous solids, based on topology- and statistics-governed rules of three-dimensional sphere packing which leads to structures with no short-, mid- or long-range order. Consequently, this model is suited to optimally represent amorphousness without having to resort to inappropriate concepts from crystallography. The general model is then concretized to the description of specific compounds in the four fundamental classes of amorphous solids such as Ni-Nb, Zr-Cu, Fe-P, SiO2, Ge-As-Se as well as amorphous polyethylene and poly(methyl)methacrylate, emphasizing its versatility and descriptive power. Application examples indicate the abundance of amorphous materials in modern-day technology, thus illustrating the importance of a better understanding of their structure and properties.