[en] In the years 1982 to 1985 the intermediate bosons W^+- and Z⁰ were detected in all the leptonic decay channels. In the present work we examined experimentally the production of the Z⁰ in proton-antiproton collisions, followed by decay of the Z⁰ into two muons. At present this is possible only in the UA1 experiment. Within the framework of this work I was initially responsible for the correct data readout from the muon detector. For this purpose it was necessary to build a monitoring system based on microprocessors, which could be used to monitor and test our apparatus. This monitoring system contains numerous programs for the diagnosis of the equipment. In the analysis I first selected the Z⁰ events in the runs of 1984 and 1985, and then determined the efficiency of this selection. I also participated in setting up the p/sub t//sup μ/ > 15 GeV/c selection. Then the Z⁰ sample was tested for completeness, and the background calculated anew. The methods of energy balance and mass fitting were refined and systematized. Thus the production properties and the mass of the Z⁰ could be determined for the first time for the entire measurement period of the UA1. The determination of the parameters of the standard model was done by also including the results of analyses from other decay channels of the W and Z bosons. 149 refs., 60 figs., 14 tabs