This chapter explains the fundamental elements of optimization problems, focusing on their structure and formulation. It introduces the essential concepts of design variables, objective functions, and constraints, which define the search space and guide solution strategies. Deterministic and heuristic approaches are discussed, along with the challenges of nonlinearity, multiple objectives, and large-scale applications in structural engineering. The chapter emphasizes the importance of properly defining optimization problems to ensure meaningful and feasible solutions. Illustrative examples demonstrate how mathematical modeling translates real-world engineering requirements into optimization frameworks. By establishing the theoretical underpinnings of optimization, the chapter intends to provide the necessary background for understanding advanced methods and applications in subsequent chapters, ensuring that the reader is prepared to approach practical structural problems with a solid conceptual foundation.