What is The Hertzsprung–Russell diagram?

Plot stars by surface temperature (hot on the left, by convention) against luminosity, both from Chapter 20’s blackbody laws, and they refuse to scatter: ninety percent crowd onto the main sequence, the diagonal band of hydrogen-burners, ordered purely by mass — heavier means hotter and disproportionately brighter ($L \propto M^{3.5}$), hence shorter-lived ($t \propto M/L \propto M^{-2.5}$: Exercise 27.4). Off the band live the plot’s exceptions and endings: cool but enormous giants (top right), and hot but tiny white dwarfs (bottom left) — because at fixed temperature, by $L = 4\pi R^2\sigma T^4$, luminosity is a measure of size. The HR diagram is not a map of kinds but of ages: a star’s dot drifts across it as its fuel runs down.