Hyperbolic Geometry, Part 1: The Upper Half-Plane and Why It Runs Number Theory

Notes from working through Ratcliffe alongside Silverman and Diamond–Shurman. What hyperbolic geometry actually is, why the metric $$ds^2 = (dx^2 + dy^2)/y^2$$ is essentially the entire theory, and how $$PSL_2(\mathbb{R})$$ ends up running everything.