A calculation is made of the coefficient of thermal expansion of metals at low temperatures, using the model of a one-component electron fluid with arbitrary dispersion law. The conditions under which the coefficient can be negative are established. Quantum oscillations of the coefficient in a quantizing magnetic field are investigated, and it is shown that they can reach large values at their peaks and have an anomalous temperature dependence which basically depends on whether oscillations are observed on a maximum or minimum Fermi surface.