Introduction to higher-spin theories

These lecture notes are based on a six-hour lecture given at the 2022 edition of the Modave Summer School in Mathematical Physics. They are meant to be an introductory course to higher-spin theories. We start with the basics of group theory allowing one to define higher-spin fields, then discuss the free theory in the metric-like and the frame-like formulations. We end with the construction of higher-spin symmetry algebras and emphasise the link between them and the free theory, as well as the considerations that allow one to construct the former from the symmetries of the latter.