Pseudo-Riemannian Geometry and General Relativity: A Short Introduction

Einstein's theory of general relativity is, fundamentally, a theory about the geometry of the universe. The mathematical framework for the theory is found in the study of pseudo-Riemannian geometry, a generalization of, the much more commonly studied, Riemannian geometry. The first half of this thesis is devoted to the study of pseudo-Riemannian geometry, and in the remaining half we study general relativity itself as well as a few classical applications of the theory.