One year of Z- and WW-Threshold running of TESLA can provide the
possibility to measure electroweak precision observables to an
extremely high accuracy. At the Z peak O(10^9) Z bosons and about 6
times 10^8 b quarks can be collected. We employ the expected
uncertainties Delta(M_W) = 6 MeV and Delta(sin^2 theta_eff) = 0.00001
and demonstrate in this way that very stringent consistency tests of
the Standard Model (SM) and the Minimal Supersymmetric Standard Model
(MSSM) will be possible. The indirect determination of the
Higgs-boson mass within the SM can reach an accuracy of about 5 %.
The 6 times 10^8 b quarks can be used to investigate various b physics
topics.