QCD CORRECTIONS TO THE E(-) CROSS-SECTION AND THE Z-BOSON DECAY-RATE - CONCEPTS AND RESULTS()E()

QCD corrections to the electron positron annihilation cross section in to hadrons and to the hadronic Z boson decay rate are reviewed. Formal developments are introduced in a form particularly suited for practic al applications. These include the operator product expansion, the hea vy mass expansion, the decoupling of heavy quarks and matching conditi ons. Exact results for the quark mass dependence are presented wheneve r available, and formulae valid in the limit of small bottom mass (m(b )(2) much less than s) or of large top mass (m(t)(2) much greater than s) are presented. The differences between vector and axial vector ind uced rates as well the classification of singlet and nonsinglet rates are discussed. Handy formulae for all contributions are collected and their numerical relevance is investigated. Prescriptions for the separ ation of the total rate into partial rates are formulated. The applica bility of the results in the low energy region, relevant for measureme nts around 10 GeV and below, is investigated and numerical predictions are collected for this energy region.