  The process of $e^+ e^-$ annihilation into $\pi^+ \pi^-$ pair with radiation
of the photon is considered. The amplitude of the reaction $e^+ e^- \to \pi^+
\pi^- \gamma$ consists of the model independent initial-state radiation (ISR)
and model dependent final-state radiation (FSR). The general structure of the
FSR tensor is constructed from Lorentz covariance, gauge invariance and
discrete symmetries in terms of the three invariant functions. To calculate
these functions we apply Chiral Perturbation Theory (ChPT) with vector and
axial-vector mesons.
  The contribution of $e^+ e^- \to \pi^+ \pi^- \gamma$ process to the muon
anomalous magnetic moment is evaluated, and results are compared with the
dominant contribution in framework of a hybrid model, consisting of VMD and
point-like scalar electrodynamics.
  The developed approach allows us also to calculate the $\pi^+ \pi^-$ charge
asymmetry.
