In this talk I will briefly go over the representation theory of split reductive groups before defining the spherical Hecke algebra and stating the classical Satake isomorphism. I will then define the affine Grassmannian, describe its geometry, and construct the Satake category. Lastly, I will state the Geometric Satake Equivalence and, with time permitting, give an overview of the main steps of the proof. This talk is intended for those with an understanding of algebraic geometry and a familiarity with the theory of split reductive linear algebraic groups.