From a mathematical viewpoint, general relativity (GR) lies at the intersection of differential geometry and partial differential equations. It is the study of manifolds whose curvature obeys certain properties (dictated by the Einstein equations), and also of various quantities of interest on these manifolds. These quantities usually have physically significant interpretations, and it is interesting to study how these quantities are affected by the underlying spacetime curvature. Since GR is a nonlinear theory, the quantities themselves also influence the underlying curvature. This talk will be an introduction to the mathematical side of GR, viewed from the lens of differential geometry and analysis.