Galaxy clusters are the largest well defined objects in the Universe which form from density fluctuations originating from the early Universe. They are interesting large-scale astrophysical laboratories for the study of a wealth of phenomena on one hand, and their evolution and abundance represent an excellent probe to test cosmological models that can describe our Universe on the other hand. In the talk I will illustrate this potential of galaxy cluster research with three examples. X-ray observations of the intracluster medium allow us to probe the chemical composition of the intracluster medium, which contains more than half of the products of stellar nucleosynthesis. A comparison of the abundances of the most important heavy elements leads very roughly to a consistent picture with our theoretical understanding of supernova yields. The second example concerns the interaction of AGN jets at the center of clusters with the intracluster medium. This "AGN feedback mechanism" prevents the gas in the centers of clusters from catastrophic cooling. This well observed scenario in galaxy clusters has shaped the modelling of feedback effects in theoretical studies of galaxy evolution.

Based on the largest X-ray galaxy cluster sample with a well defined
selection function from the ROSAT All-Sky Survey we obtain measures
of the large-scale structure of the Universe which allow us to
test cosmological models. The parameters which are best determined
by our survey are the cosmic matter density and the amplitude of the
matter density fluctuations today. We discuss these results in
context with other observational constraints of cosmological
parameters. We also use the clusters to map the large-scale
matter distribution in the local Universe.