String theory is a framework of physics which in particular gives rise to various interesting predictions in mathematics. Some of the more interesting predictions are derived from so-called S-duality, which provides a non-trivial equivalence of two physical theories. The main aim of the talk is to explain how to mathematically understand aspects of string theory, focusing on topological strings, and discuss S-duality in the context. A large part of the talk will be devoted to providing a dictionary between string theory and mathematical objects.  This talk is based on a joint work with Surya Raghavendran.