Geometric Group Theory is the practice of connecting properties of groups to the properties of topological spaces with intrinsic connections to those groups. This has yielded many deep results across the study of infinite groups. In this talk, we will demonstrate how groups and topological spaces are interlinked, observe how algebraic properties of groups can be derived from the properties of topological spaces, and explore how we can use the local structure of topological spaces to draw conclusions about the global structure of those spaces, allowing us to calculate further properties of groups.