A study of the $\tau$ Lepton polarization in $Z^0$ decays

Tau polarization in the decay Z° -* t+t ~ channel is studied in this work. Z° events were collected by the ALEPH detector at the LEP collider at CERN, Geneva. The data collected by the detector were in a range of energy in the vicinity of the Z° pole. D ata analysis in the ALEPH Collaboration is achieved through the contribution of many people from various institutes spread all over the world, since the idea of LEP was born. The author's contributions to the experiment include work on the construction and testing of the electromagnetic calorimeter modules built at Glasgow University, as well as the analysis presented here. The analysis presented in this thesis is the individual work of the author within a team in the ALEPH Collaboration. No portion of this thesis has been subm itted in support of an application for another degree or qualification in this University, or any other institution of teaching.