A fundamental idea in algebraic geometry is the correspondence between divisors (roughly speaking, codimension-1 subvarieties) and line bundles. Though not so difficult to state, the consequences of this correspondence are far-reaching, underpinning areas as diverse as intersection theory and birational geometry.
In this talk we will try to explain this concept and some of its applications, restricting for the most part to smooth algebraic varieties. Time permitting, we will then move on to the nonsmooth case and explore an important subtlety which arises there: the distinction between Cartier and Weil divisors.