  Given a sample from a discretely observed L\'evy process $X=(X_t)_{t\geq 0}$
of the finite jump activity, the problem of nonparametric estimation of the
L\'evy density $\rho$ corresponding to the process $X$ is studied. An estimator
of $\rho$ is proposed that is based on a suitable inversion of the
L\'evy-Khintchine formula and a plug-in device. The main results of the paper
deal with upper risk bounds for estimation of $\rho$ over suitable classes of
L\'evy triplets. The corresponding lower bounds are also discussed.
