How do you build gravity by squaring a simpler force?

These course notes walk through the idea that gravity is, in a precise mathematical sense, the square of a gauge theory like electromagnetism — a relationship called the double copy. The notes cover both on-shell and off-shell versions of this correspondence, ending with how it fits inside T-duality-invariant frameworks. Aimed at graduate students, they're a self-contained entry point to a technique increasingly used to simplify gravitational wave calculations.