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The observations reported here of the electron spin resonance in quite perfect single crystals of graphite clearly establish that the resonance arises from mobile charge carriers. The line shape is of the Dysonian form which is characteristic of conduction electron spin resonance in metals. The intensity of the spin resonance agrees, both in absolute magnitude and in temperature dependence, with values calculated from the band model of graphite by McClure. The $g$ value of the resonance shows a remarkably large anisotropy which depends strongly on temperature and on the position of the Fermi level with respect to the band edge. At room temperature in pure graphite, $g$ varies from 2.0026\ifmmode\pm\else\textpm\fi{}0.0002 to 2.0495\ifmmode\pm\else\textpm\fi{}0.0002 as the magnetic field is shifted from perpendicular to parallel to the $c$ axis. The $g$-value anisotropy increases with decreasing temperature; ${g}_{\mathrm{II}}$ becomes 2.127 at 77\ifmmode^\circ\else\textdegree\fi{}K while ${g}_{\ensuremath{\perp}}$ remains constant. The line width of the resonance is a few gauss (${T}_{2}=2.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ sec) which is extremely narrow in comparison with the field shifts caused by changes of anisotropy with temperature. This indicates that for conduction states in graphite, the $g$ value is a strong function of the wave vector and that the line is narrowed by an averaging process in $k$ space. This averaging is similar to that which occurs in motional and exchange narrowing.