We will learn Einstein's Theory of General Relativity and apply it to neutron stars and black holes---compact objects at the frontier of human knowledge about the fundamental nature of space, time, and matter. John Wheeler famously characterized General Relativity as saying, "Space tells matter how to move. Matter tells space how to curve." The theory is written in the language of differential geometry, so along the way to articulating and using the theory, we will introduce mathematical constructs from this branch of mathematics. We will necessarily develop our formal mathematical reasoning ability, and both linear algebra and multi-variate calculus will serve as essential background knowledge. At the same time, we will take a *physics first* approach, and introduce needed differential geometry concepts gradually, applying them to physics problems at each earliest opportunity. Toward the end of the course, using knowledge gained in the first portion of the class, students will work on projects relating to contemporary research on black holes or neutron stars. May be elected as Physics 301. Distribution area: none. Prerequisites: Mathematics 225 and Physic 156. Corequisites: Mathematics 240 and Physics 245.