The Gauss-Bonnet theorem is a beautiful result about surfaces in 3-dimensional space which bridges two fields of mathematics: geometry and topology. We will begin by learning a bit about surfaces in 3-space, the Euler characteristic, and what it means for two surfaces to be "the same". We will also discuss what it means for a surface to have "curvature" and how one might go about quantifying just how curved a surface really is. Last, we will see how the Gauss-Bonnet theorem brings all these ideas together, and talk about several surprising consequences of this fact.