The γ-ray emission above $250 \mathrm{GeV}$ from the BL Lac object Markarian 421 was observed by the CAT Cherenkov imaging telescope between December, 1996, and June, 2000. In 1998, the source produced a series of small flares, making it the second extragalactic source detected by CAT. The time-averaged differential spectrum has been measured from 0.3 to $5 \mathrm{TeV}$, which is well fitted with a power law: $\frac{\mathrm{d}\phi}{\mathrm{d}E}\varpropto E_{\mathrm{TeV}}^{-2.88\pm0.12^\mathrm{stat}\pm0.06^\mathrm{syst}}$. In 2000, the source showed an unprecedented activity, with variability time-scales as short as one hour, as for instance observed during the night between 4 and 5 February. The 2000 time-averaged spectrum measured is compatible with that of 1998, but some indication of a spectral curvature is found between 0.3 and $5 \mathrm{TeV}$. The possibility of $\mathrm{TeV}$ spectral hardening during flares is also discussed, and the results are compared to those obtained on the other $\mathrm{TeV}$ BL Lac, Markarian 501.