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This chapter starts with some brief historical overview of optimization followed by four subsections devoted to the formulation and reformulation of optimization problems. The subsequent two sections revisit basic tools of mathematical analysis and matrix analysis, which will be frequently used along the book. Next we revisit the local optimality conditions for functions of several variables (also called multivariate) at interior points of their domains that are usually studied in courses on differential calculus. Then we introduce the concept of coercive function, which is used to prove the existence of global minimum of continuous functions on unbounded domains.