In his Ph.D. thesis, Greg McShane proved that a certain sum indexed over the simple closed geodesics on a (hyperbolic) punctured torus is equal to a constant independent of the metric. This metric-independence can be understood to mean that this sum is a constant function on the moduli space M_{1,1} of hyperbolic metrics on the punctured torus. McShane's proof gives very explicit geometric insight into punctured tori, and the primary goal of this talk is to convey as much of that geometric insight as possible. We will also discuss Mirzakhani's method of integrating McShane's identity, by passing to an infinite cover of M_{1,1}, in order to calculate the volume of M_{1,1} with respect to the Weil-Petersson form. Speaker(s): Bradley Zykoski (UM)