This novel interpretation of the relationship between space, time, and gravitation and its cosmological implications is based on the author's discovery of a small but significant value in gravitation that was overlooked by both Newton and Einstein. Dubbed the Burke Potential, it resolved an issue with gravitation measurements and rates of entropy related to the discovery of a time-varying part of the local gravitational field. The treatment provides many examples and applications to the geometric language and ideas that are essential to modern theoretical physics. Nearly every section concludes with a selection of problems. Prerequisites include a familiarity with linear algebra, ordinary differential equations, and special relativity. For graduate-level educators and students in physics, relativity, astrophysics, and cosmology. AUTHOR: William L. Burke (1941 96) was an astronomy, astrophysics, and physics professor at University of California, Santa Cruz. He is the author of two books: Spacetime, Geometry, Cosmology and Applied Differential Geometry. Burke gained his baccalaureate at California Institute of Technology in 1963. His doctorate was supervised by leading physicists Richard Feynman and John Wheeler. Burke discovered an aspect of gravitation overlooked by Einstein, which was named the Burke Potential. He became a full professor at UCSC in 1988. A rising star of the new physics, his life was cut short by injuries suffered from an automobile accident.