This chapter moves from the intuitive ideas of Optimization presented in the first chapter to the formal mathematical language required for its detailed study and application. Therefore, this chapter provides the fundamentals required to work with Optimization problems in academic and professional environments. Here, we systematically define the main building blocks of optimization problems, including variables (scalar and vector, covering continuous, discrete, and mixed types), equality and inequality constraints, and functions, detailing their properties such as linearity, non-linearity, and convexity. We also cover the difference between Single-Objective and Multi-Objective Optimization and discuss the formal definition of solutions, including concepts like the feasible region, feasible and infeasible points, local and global optima, Pareto dominance, and the Pareto front.