  We discuss the electroweak gauge symmetry breaking triggered by a new strong
attractive interaction to condensate fermion-antifermion, and topcolor is a
prototype. To deal with the fermion pairing, a general method based on the
Hubbard-Stratonovich transformation in the functional integral approach is
used.
  We derive a formula which relates the $W^\pm$, $Z^0$ weak boson masses to
that of the condensated fermion, thus generalizing the Pagels-Stokar formula
obtained in QCD. The custodial SU(2) electroweak symmetry turns out to be
systematically violated, the deviation of $\rho\equiv
M_W^2/(M_Z^2\cos^2\theta_W) $ from unity is related to the new physics scale
$\Lambda$. Some phenomenological consequences of the top-pair condensation
models are discussed. Distinctive signatures of the $\bar{t}t$ scalar bound
state, a Higgs boson like denoted by $H_t$, are the dominant decay modes
$H_t\to \Upsilon +\gamma ,$ $H_t\to \Upsilon +Z^0$, and $H_t \to B^*
+\bar{B}^*$.
