This course aims to equip the student with advanced mathematical tools from differential geometry, essential for research in modern Theoretical Physics.

More specifically, the notation of differential forms will be introduced and the geometric aspects of gauge theory will be explored. Gravity will be interpreted as a gauge theory in this geometric setting. Manifolds will be studied, leading to the definition of fibre bundles. Finally, we will explore the Dirac and 't Hooft-Polyakov monopoles as well as the Yang-Mills instanton, and their associated description in fibre bundle language.