  We present numerical results on the recently completed $O(\alpha^2)$ initial
state corrections to the process $e^+e^- \rightarrow \gamma^*/Z^*$, which is a
central process at past and future high energy and high luminsoity colliders
for precision measurements of the properties of the $Z$-boson, the Higgs boson,
and the top quark. We observe differences to an earlier result
\cite{Berends:1987ab} in the non-logarithmic contributions at $O(\alpha^2)$.
The new result leads to a 4 MeV shift in the $Z$ width considering the lower
end $s_0 = 4 m_\tau^2$ of the radiation region, which is larger than the
present accuracy. We present predictions on the radiative corrections to the
central processes $e^+e^- \rightarrow \gamma^*/Z^*$, $e^+e^- \rightarrow Z H$
and $e^+e^- \rightarrow t \overline{t}$ planned at future colliders like the
ILC, CLIC, Fcc\_ee and CEPC to measure the mass and the width of the $Z$ boson,
the Higgs boson and the top quark, for which the present corrections are
significant.
