  Scalar-tensor theory of gravity with nonlinear electromagnetic field,
minimally coupled to gravity is considered and static black hole solutions are
obtained. Namely, power-law and Born-Infeld nonlinear Lagrangians for the
electromagnetic field are examined. Since the cosmological constant is taken
into account, it allowed us to investigate so-called topological black holes.
Black hole thermodynamics is studied, in particular temperature of the black
holes is calculated and examined and the first law of thermodynamics is
obtained with help of Wald's approach.
