The chapter introduces the concept of optimization and its related mathematical treatment. A basic analysis in one dimension is considered, showing a number of illustrative situations, including the effect of bounds. This analysis is then extended to several dimensions, where gradients and hessians are used. A short section comes now for introducing useful MATLAB functions. The chapter ends with some examples (including least-squares fitting) and a summary of the MATLAB Symbolic Toolbox. Several short programs in MATLAB were embedded in the text.