One of the intriguing questions in materials science is how elements can be combined to form a solid with desired properties. One part of the answer to this question can be derived from the fundamental relationship between the composition, structure, and basic bonding in materials. This lecture starts with a description of the fundamental atomic structure connected to the structure stability and correlated properties. These aspects will be covered in the context of thermodynamics, crystallography, and solid state physics that complete the correlations between the structures and properties and beyond. Pursuing the discovery and development of advanced material systems lies in this deep understanding of the materials fundamentals, which is also crucial to achieving global competitiveness of material research.