We present results obtained from a study of the structure of hadronic events recorded by the L3 detector at various centre-of-mass energies. The distributions of event shape variables and the energy dependence of their mean values are measured from 30 GeV to 189 GeV and compared with various QCD models. The energy dependence of the moments of event shape variables is used to test a power law ansatz for the non-perturbative component. We obtain a universal value of the non-perturbative parameter α0 = 0.537 ± 0.073. From a comparison with resummed (αs2) QCD calculations, we determine the strong coupling constant at each of the selected energies. The measurements demonstrate the running of αs as expected in QCD with a value of αs(mZ) = 0.1215 ± 0.0012 (exp) ± 0.0061 (th).