  We study thermodynamics and phase transitions of magnetically charged by
nonlinear electrodynamics (NED) Anti-de Sitter (AdS) black holes in an extended
phase space. The cosmological constant is treated as a thermodynamic pressure
whereas the black hole mass is considered such as the chemical enthalpy. The
horizon thermodynamics of black holes shows an analogy with the Van der Waals
liquid-gas system. We define a quantities which are conjugated to the parameter
of NED and a magnetic charge. It is shown that the first law of thermodynamics
and the generalized Smarr relation hold. The critical exponents are the same as
in the Van der Waals system. The Joule--Thomson adiabatic expansion of NED-AdS
black holes is investigated because of thermodynamic behavior of black holes.
The Joule--Thomson coefficient, the inversion and isenthalpic curves are
discussed. The minimum of inversion temperature and the corresponding event
horizon radius are obtained.
