  Metallic strontium titanate (SrTiO$_3$) is known to have both normal-state
and superconducting properties that vary strongly over a wide range of charge
carrier densities. This indicates the importance of nonlinear dynamics, and has
hindered the development of a clear qualitative description of the observed
behaviour. A major challenge is to understand how the charge carriers
themselves evolve with doping and temperature, with possible polaronic effects
and evidence of an effective mass that strongly increases with temperature.
Here we use $^{47,49}$Ti nuclear magnetic resonance (NMR) to perform a
comprehensive study of the electronic spin susceptibility in the dilute
metallic state of strontium titanate across the doping-temperature phase
diagram. We find a temperature-dependent Knight shift that can be
quantitatively understood within a non-degenerate Fermi gas model that fully
takes into account the complex band structure of SrTiO$_3$. Our data are
consistent with a temperature-independent effective mass, and we show that the
behavior of the spin susceptibility is universal in a wide range of
temperatures and carrier concentrations. These results provide a microscopic
foundation for the understanding of the properties of the unconventional
low-density metallic state in strontium titanate and related materials.
