The bonding and physical properties of elemental substances (pure elements) are first examined using quantum chemical bonding theory. This is followed by a theoretical discussion on whether an alloy can be formed between two elements—specifically, whether the alloying element is solid soluble or insoluble in the solvent element. This determination can be made based on the atomic bond population (ABP) and atomic population (AP). If the ABP and AP values of the alloying element are close to those of the solvent, the element is considered to be solid soluble; if they differ significantly, the element is considered insoluble. In well-mixed solid solutions, the cohesive energy typically varies linearly with composition. A substantial increase in cohesive energy suggests compound formation, whereas a significant decrease implies insolubility. For Al, Fe, and Mg alloys, the stability of alloying elements is evaluated by combining cohesive energy and its fluctuation with ABP and AP, thereby clarifying their solid solubility, insolubility, and tendency to form compounds. Based on these theoretical principles, alloy types can be categorized into six groups: solid-solution-hardening, age-hardening, work-hardening, corrosion-resistant, heat-resistant, and castable types. Each category is discussed in terms of its definition, bonding characteristics, and electronic structure.