Loop groups are infinite-dimensional Lie groups arising naturally in a variety of situations. Their representation theory is closely tied to conformal field theory, while the geometry of loops groups can be related to integrable systems and harmonic maps. In this talk we will discuss some of the mathematical prerequisites underlying the aforementioned applications in mathematical physics, following the book by Pressley-Segal. We will come across an interesting connection between loop groups and moduli spaces of holomorphic vector bundles on a Riemann surface. Moreover we will see how the theory of loop groups sheds some light on Bott periodicity.