High precision tests of QCD at LEP

In this report, the latest measurements involving high precision tests of QCD at LEP are reviewed. The status of the strong coupling constant, αs, is discussed and summarized. The relative ratio of the normalized three-jet cross-section of b and light, l=u1d,s, quarks has been determined by the DELPHI collaboration in agreement with the QCD prediction including NLO radiative corrections with mass effects. In this study the running b quark mass at the MZ scale has been measured providing the first experimental evidence of the running of the b quark mass. As a consequence of this study the flavour independence of αs for b and l quarks is established within 1% accuracy. The charged multiplicity of quark and gluon jets has been investigated for various three-jet event topologies and compared for different energy and transverse momentum-like scales. An increase of the gluon jet multiplicity with the scale was observed and this was twice as strong as the corresponding increase for quarks