Hard scattering. perturbative QCD

The more accurate results of recent high energy scattering experiments require more precise theoretical predictions. Within the framework of perturbative QCD one can systematically improve the accuracy of the predictions by calculating more and more higher order corrections. In the last years an impressively large number of higher order corrections have been calculated. Several of these calculations are rather complex and their successful completions required numerous technical improvements. In Section 2 we discuss a simple derivation of the KNL cancellation theorem using concepts such as pinch singularities and Landau equations. Its generalizations to jet production is also discussed. We also consider in this section the next-to-next-to leading order description of the e+e- annihilation cross section and the measurements of αS from the LEP data. Section 3 is devoted to a discussion of nature of perturbative QCD in terms of Borel transforms. The theoretical issues concerning three jet like quantities at LEP are considered in section 4. The fundamental formula of the QCD improved parton model giving the physical cross sections of hadron-hadron hard scattering process to any fixed order of perturbative QCD is given in section 5. Its use is illustrated on the example of jet production. Finally section 6 is devoted to a brief discussion of some of the basic technical tools (helicity method, use of supersymmetry, dimensional reduction, background gauge etc.) used and invented recently for calculating next-to-leading order corrections to four, five and six leg amplitudes. (author) figs., tabs., refs