  These notes have been prepared as reading material for the mini-course given
by the author at the "2019 Graduate Summer School" at Park City Mathematics
Institute - Institute for Advanced Study. We begin by introducing Higgs bundles
and their main properties (Lecture 1), and then we discuss the Hitchin
fibration and its different uses (Lecture 2). The second half of the course is
dedicated to studying different types of subspaces (branes) of the moduli space
of complex Higgs bundles, their appearances in terms of flat connections and
representations (Lecture 3), as well as correspondences between them (Lecture
4).
