Radiative Corrections for e+e- Collisions

In recent years the Standard Model of electroweak interactions has successfully passed a number of crucial tests, most notably in neutral current reactions and through the observation of W- and Z-bosons in proton-antiproton collisions. How ever, experiments are only beginning to verify one of the most basic consequences of its theoretical formulation as a local quantum field theory: quantum corrections as calculated in perturbation theory. Measurements that will be carried out at electron positron colliders at Stanford and CERN in the very near future will improve the accuracy by more than an order of magnitude. Thus either these crucial elements of the present theoretical framework will be confirmed or the road to physics beyond the Standard Model will be opened. A huge amount of theoretical work has been invested during the past few years to match the envisaged experimental precision. QED corrections, in particular from initial state radiation, will playa dominant role in the interpretation of measurements and have to be understood at a hitherto unrivalled level of accuracy. Analytical cal culations - either to a fixed order in a or by summing large logarithms to arbitrary order - are complementary to recent developments of Monte Carlo techniques in the simulation of events with multiple photon emission. Measurements with hadronic final states evidently require the understanding of hadronic corrections to high accu racy. Even purely leptonic reactions are influenced by hadronic interactions through vacuum polarization.