In a group, we may use a normal subgroup to form a quotient that is also a group, the elements of which are the equivalence classes. Can we use a group to form equivalence classes on a manifold to produce a manifold? We choose a group, G, a manifold M, and a point p on M. We see which points can be arrived at from p(this is called the orbit of p under G). In this talk, we explore specific group actions on particular manifolds and try to determine what the orbit spaces are. We define what it means for a set to be a differentiable manifold and we introduce the Quotient Manifold Theorem, which gives sufficient conditions for the orbit space to be a differentiable manifold. A good understanding of linear algebra and calculus are required. A knowledge of topology may help with the technical parts of the talk.