  The production of the three normal neutrinos via $e^-e+$ collision at
$Z$-boson peak (neutrino production in a Z-factory) is investigated thoroughly.
The differences of $\nu_e$-pair production from $\nu_\mu$-pair and
$\nu_\tau$-pair production are presented in various aspects. Namely the total
cross sections, relevant differential cross sections and the forward-backward
asymmetry etc for these neutrinos are presented in terms of figures as well as
numerical tables. The restriction on the room for the mixing of the three
species of light neutrinos with possible externals (heavy neutral leptons
and/or stereos) from refined measurements of the invisible width of $Z$-boson
is discussed.
