  In these lecture notes we will try to give an introduction to the use of the
mathematics of fibre bundles in the understanding of some global aspects of
gauge theories, such as monopoles and instantons. They are primarily aimed at
beginning PhD students. First, we will briefly review the concept of a fibre
bundle and define the notion of a connection and its curvature on a principal
bundle. Then we will introduce some ideas from topology such as homotopy,
topological degree and characteristic classes. Finally, we will apply these
notions to the bundle setup corresponding to monopoles and instantons. We will
end with some remarks on index theorems and their applications and some hints
towards a bigger picture.
