  The Lovelock gravity consists of the dimensionally extended Euler densities.
The geometry and horizon structure of black hole solutions could be quite
complicated in this gravity, however, we find that some thermodynamic
quantities of the black holes like the mass, Hawking temperature and entropy,
have simple forms expressed in terms of horizon radius. The case with black
hole horizon being a Ricci flat hypersurface is particularly simple. In that
case the black holes are always thermodynamically stable with a positive heat
capacity and their entropy still obeys the area formula, which is no longer
valid for black holes with positive or negative constant curvature horizon
hypersurface. In addition, for black holes in the gravity theory of Ricci
scalar plus a $2n$-dimensional Euler density with a positive coefficient,
thermodynamically stable small black holes always exist in $D=2n+1$ dimensions,
which are absent in the case without the Euler density term, while the
thermodynamic properties of the black hole solutions with the Euler density
term are qualitatively similar to those of black holes without the Euler
density term as $D>2n+1$.
