The four experiments, ALEPH, DELPHI, L3 and OPAL at LEP, have performed a large number of precise measurements to test Quantum Chromodynamics. The strong coupling constant has been measured with high precision:α_s(M_z) = 0.123±0.004. The coupling constant has been found to be independent of quark flavour. The running ofα_s has been demonstrated by the data. Second order QCD matrix element calculations have been tested from several measured distributions in 3-jet and 4-jet events. These distributions give evidence of the vector nature of the gluon and provide measurements of the QCD colour factors. The hadronic distributions are well reproduced by QCD Monte Carlo programs as well as by analytical calculations with soft gluon coherence effects.

Several studies have been made to the hadronic final states in e⁺e⁻ collisions at LEP. Studies of the annihilation process at LEP2 have given rise to results on jet rate, event shape, heavy flavour production, inclusive momentum spectra, Bose-Einstein correlation and colour reconnection effects. Event shape studies have given rise to accurate determination of the strong coupling constant α_s using O (α_s²) with resummed leading and next-to-leading log calculation and also with power law corrections. Studies of 2-photon processes have yielded results on γγ cross-section, heavy flavour production, photon structure function and γ*γ* scattering.

We consider the effects of quark masses to the perturbative thrust in e⁺e⁻ annihilation. In particular we show that perturbative power corrections resulting from non-zero quark masses considerably alters the size of the non-perturbative power corrections and consequently, significantly changes the fitted value of α_s.

The strong coupling constant, α_s, has been determined from many pure inclusive and semi-inclusive measurements. All these measurements, measured at different scales, are consistent among each other and the measurements can be combined to give α_s(mz)= 0.118±0.003.

This is summary of the activities of the working group on collider physics in the IXth Workshop on High Energy Physics Phenomenology (WHEPP-9) held at the Institute of Physics, Bhubaneswar, India in January 2006. Some of the work subsequently done on these problems by the subgroups formed during the workshop is included in this report.