This will be an introduction to geometric topology, a field of mathematics concerned with topological properties of manifolds. We will study both topological and smooth manifolds, and prove some fundamental results about them (like the Schoenflies theorem, the generalised Poincaré conjecture, the existence of exotic smooth structures), several of which have been awarded with Fields medals.

This will be an introduction to geometric topology, a field of mathematics concerned with topological properties of manifolds. We will study both topological and smooth manifolds, and prove some fundamental results about them (like the Schoenflies theorem, the generalised Poincaré conjecture, the existence of exotic smooth structures), several of which have been awarded with Fields medals.