We begin by defining the affine Grassmannian of a given (complex, connected) reductive group. It is known that the affine Grassmannian decomposes into a union of finite-dimensional subvarieties, known as Schubert cells, and the closures of these cells form projective varieties. As both a key example and viewpoint, we will interpret the affine Grassmannian of GL_n​ as a space of lattices. To lay the groundwork for discussing perverse sheaves and the Geometric Satake equivalence, I will also introduce the concept of local systems in a concise and minimal way.