This chapter aims at providing an introduction to numerical optimization with some applications in astronomy and astrophysics. We provide important preliminary definitions that will guide the reader towards different optimization procedures. We discuss three families of optimization problems and describe numerical algorithms allowing, when this is possible, to solve these problems. For each family, we present in detail simple examples and more involved advanced examples. As a final illustration, we focus on two worked-out examples of optimization applied to astronomical data. The first application is a supervised classification of RR-Lyrae stars. The second one is the denoising of galactic spectra formulated by means of sparsity inducing models in a redundant dictionary.