  The charged current (anti)neutrino induced eta production from the nucleons
is studied in a model based on the effective Lagrangians to evaluate the
contribution from the nonresonant and resonant diagrams. The contribution from
the nonresonant background terms has been obtained using a microscopic model
based on the SU(3) chiral Lagrangians. The contribution from the resonant
diagrams due to the low lying $S_{11}(1535)$, $S_{11} (1650)$, and $P_{11}
(1710)$ resonances has been evaluated using an effective phenomenological
Lagrangian with its parameters determined from the experimental values of their
branching ratios and decay widths to the $N\eta$ channel. The model is first
used to reproduce satisfactorily the experimental data from the MAINZ and JLab
on the total cross sections for the photo- and electro- production of $\eta$
mesons, which fixes the model parameters in the vector current interaction. The
PCAC hypothesis and generalized Goldberger-Treiman relation are used to fix the
parameters of the axial vector interaction. The model is then applied to study
the weak production of eta mesons induced by the neutrinos and antineutrinos,
and predicts the numerical values for the $Q^2$-distribution, $\eta$-momentum
distribution, and the total cross section for the reactions $\nu_{\mu} + n
\longrightarrow \mu^{-} + p + \eta$ and $\bar{\nu}_{\mu} + p \longrightarrow
\mu^+ + n + \eta$ in the energy region up to 2 GeV. It is found that the photo,
electro, and (anti)neutrino production of eta mesons is dominated by the
contribution from the $S_{11}(1535)$ resonance. The results discussed in this
work are relevant for the present and future accelerator experiments like
MicroBooNE, T2K, NOvA, MINERvA, T2-HyperK and DUNE as well as for the
atmospheric neutrino experiments.
