A primer course for incoming graduate students with non-MSE background. Basic concepts of structure and descriptors: crystalline and non-crystalline solids, compounds, solid solutions. Structural imperfections: point defects, dislocations and strain fields, surfaces, interfaces. Defects in ionic crystals. Thermodynamic underpinnings of phase diagrams: phase rule, chemical potential, equilibrium conditions, metastability. Unary systems. Fundamentals of binary systems, allotropes, invariant reactions, phase fractions and compositions, relationship with structure evolution. Maps for reacting systems, Ellingham diagrams, predominance diagrams. Introduction to ternary systems: liquidus surfaces and basic invariant reactions.