  This thesis presents a study of the decays $\tau\rightarrow
e\nu\overline{\nu}$ identified after a selection of $\tau^+\tau^-$ events
produced in $e^+e^-$ collisions at LEP. These collisions, predominantly
mediated by a $Z^0$ boson, offer a good laboratory for the study of weak
current parameters. Moreover, the decays of the tau lepton, which proceed via a
$W$ boson, increase the possibilities of our study. The experimental
observables, which imply an indirect knowledge of the coupling constants,
include the polarization asymmetry and the forward-backward polarization
asymmetry. The branching ratio of the electronic decay of the $\tau$ lepton
($18.24\pm0.28\pm0.32)\%$) derives a measurement of the strong coupling
constant $\alpha_s$ at the scale of the $Z^0$ boson mass
($0.118^{+0.004}_{-0.006}\pm0.006$) and a test of lepton universality in weak
currents ($\frac{g_{\tau}}{g_{\mu}}=1.000\pm0.014$). The spectra of momenta and
electromagnetic energy depositions used as estimates of the energy of the
electron allow to measure the polarization asymmetries
($P_{\tau}=-0.16\pm0.09\pm0.05$ and $A^{FB}_{pol}=-0.19\pm0.09\pm0.01$) giving
subsequent values for the effective $sin^2\theta_W$ ($0.230\pm0.013$ and
$0.218\pm0.015$).
