  In this paper, we obtain topological black hole solutions of third order
Lovelock gravity couple with two classes of Born-Infeld type nonlinear
electrodynamics with anti-de Sitter asymptotic structure. We investigate
geometric and thermodynamics properties of the solutions and obtain conserved
quantities of the black holes. We examine the first law of thermodynamics and
find that the conserved and thermodynamic quantities of the black hole
solutions satisfy the first law of thermodynamics. Finally, we calculate the
heat capacity and determinant of Hessian matrix to evaluate thermal stability
in both canonical and grand canonical ensembles. Moreover, we consider extended
phase space thermodynamics to obtain generalized first law of thermodynamics as
well as extended Smarr formula.
