  We consider the solution X = (Xt) t$\ge$0 of a multivariate stochastic
differential equation with Levy-type jumps and with unique invariant
probability measure with density $\mu$. We assume that a continuous record of
observations X T = (Xt) 0$\le$t$\le$T is available. In the case without jumps,
Reiss and Dalalyan (2007) and Strauch (2018) have found convergence rates of
invariant density estimators, under respectively isotropic and anisotropic
H{\"o}lder smoothness constraints, which are considerably faster than those
known from standard multivariate density estimation. We extend the previous
works by obtaining, in presence of jumps, some estimators which have the same
convergence rates they had in the case without jumps for d $\ge$ 2 and a rate
which depends on the degree of the jumps in the one-dimensional setting. We
propose moreover a data driven bandwidth selection procedure based on the
Goldensh-luger and Lepski (2011) method which leads us to an adaptive
non-parametric kernel estimator of the stationary density $\mu$ of the jump
diffusion X. Adaptive bandwidth selection, anisotropic density estimation,
ergodic diffusion with jumps, L{\'e}vy driven SDE
