This theoretical work incorporates relativistic gravity and relativistic cosmology in an effort to understand the effects of a non-vanishing cosmological constant Λ on the universe. After a brief historical review of contemporary models of the universe, Einstein's theory of general relativity is introduced. In particular, following an introduction to tensor calculus and Riemannian geometry, Einstein's field equations with the cosmological term are developed. Then assuming a simple, but reasonable model of the universe, Einstein's field equations are reduced to a single differential equation known as Friedmann's equation, which is solved via numerical integration. Finally, the recent experimental cosmological data are reviewed and discussed in terms of the geometry and expansion of the universe.