  By running the prospective high-energy e^+e^- collider TESLA in the GigaZ
mode on the Z resonance, experiments can be performed on the basis of more than
10^9 Z events. This will allow the measurement of the effective electroweak
mixing angle to an accuracy of \delta sin^2(theta_W,eff) \approx \pm 10^-5. The
W boson mass is likewise expected to be measurable with an error of \delta M_W
\approx \pm 6 MeV near the W^+W^ threshold. We review the electroweak precision
tests that can be performed with these high precision measurements within the
Standard Model (SM) and its minimal Supersymmetric extension (MSSM). The
complementarity of direct measurements at a prospective linear e^+e^- collider
and indirect constraints following from measurements performed at GigaZ is
emphasized.
