In classic algebraic geometry, we want to study the zero sets of polynomials. In modern algebraic geometry, smart people develop algebraic tools and methods for studying the geometry of these zero sets. This talk is not about modern algebraic geometry. Instead, we will explore the world of complex donuts (compact Riemann surfaces) and their holomorphic and meromorphic functions. By the end of this talk, we will know a few basic results in this theory and see them in action on the Riemann sphere. Hopefully this helps to give some geometric intuition for anyone taking algebraic geometry next semester. If time permits, we may also state the Riemann-Roch Theorem in the complex curve setting and give a friendly introduction to sheaves. ????