  We analyze the formation of the redshifted hyperfine structure line 21-cm of
hydrogen atom in the Dark Ages, Cosmic Dawn, and Reionization epochs. The
evolution of the global differential brightness temperature in this line was
computed to study its dependence on the values of cosmological parameters and
physical conditions in the intergalactic medium. Variations of the depth of the
Dark Ages absorption line at $z\sim80$ with variations of the cosmological
parameters $\Omega_b$, $\Omega_{cdm}$, $\Omega_{\Lambda}$, $\Omega_K$ and $H_0$
are studied. The standard model with post-Planck parameters predicts a value of
the differential brightness temperature in the center of the absorption line
$\sim$30-50 mK. The profile of this line can be quite another in the
non-standard cosmological models, which include the annihilating or decaying
dark matter, a primordial stochastic magnetic field, etc. It can be shallower
or be an emission bump instead of an absorption trough. It is also shown that
the position and depth of the Cosmic Dawn absorption line formed at 10<z<30,
due to the Wouthuysen-Field effect, is mainly defined by the spectral energy
distribution of the first sources of light. If reionization occurs at
$z_{ri}=7\pm1$, then the differential brightness temperature in the center of
this line is $\sim$80 mK. During the reionization, the emission with an
amplitude of $\sim$20 mK is possible. It is also shown that the temperature,
density, and degree of ionization of the baryonic component are decisive in
calculating the intensity of the 21-cm absorption/emission line from these
epochs.
