Abstract: In this talk, I will give an overview of some of the fundamental tools used in symplectic topology, restricting to the case of Riemann surfaces. This is not only for simplicity — (symplectic) topology in this dimension has close links to the representation theory of an interesting class of algebras. The aim of this talk is to explain how symplectic topology can be used to answer difficult questions in representation theory. Time permitting, I will mention how one hopes to use representation theory to answer difficult questions in symplectic topology. There will be no background assumed for this talk.