In this talk, we look to the past and discuss the 19th century roots of modern algebraic geometry, with a particular focus on the ideas and stories of Riemann. We will see how integrals of rational functions find their way to the genus of a surface, as well as how multivalued functions naturally lead to the notion of integral closure in commutative algebra. We will also tell the story of the Riemann-Roch theorem, giving a very rough sketch of the original proof. At the end we will present Riemann's original dimension count of the moduli space of genus g curves. Speaker(s): Jonghyun Lee (UM)