This chapter introduces the core economic challenge of scarcity and the associated principle of efficiency in the use of scarce resources. Drawing on foundational definitions of economics by Robbins and others, it explores how limited resources necessitate optimal decision-making. The chapter presents mathematical programming as a tool to analyze economic behavior under resource constraints, laying the groundwork for various models relevant to households, firms, and policy contexts. By defining objective functions, feasible sets, and decision variables, the chapter establishes a general optimization framework that guides the rest of the book. The final part of the chapter provides a classification of optimization problems distinguishing between static optimization (linear and nonlinear programming, convex and nonconvex programming) and dynamic optimization (in continuous time and in discrete time).