This chapter is concerned with nonparametric estimation of the Lévy density of a Lévy process. The sample path is observed at $n$ equispaced instants with sampling interval $\Delta$. We develop several nonparametric adaptive methods of estimation based on deconvolution, projection and kernel. The asymptotic framework is: $n$ tends to infinity, $\Delta=\Delta_n$ tends to $0$ while $n\Delta_n$ tends to infinity (high frequency). Bounds for the ${\mathbb L}^2$-risk of estimators are given. Rates of convergence are discussed. Estimation of the drift and Gaussian component coefficients is studied. A specific method for the estimating the jump density of compound Poisson processes is presented. Examples and simulation results illustrate the performance of estimators.
