Rather than study the entire galaxy population, something that requires surveys very expensive in terms of telescope time, there are some advantages in concentrating only on the "peaks" of the density field, or rather those rare fluctuations that today correspond to galaxy clusters, the largest and most massive gravitationally bound structures in the Universe. Galaxy clusters are very important cosmic laboratories, in which gravitational and thermal phenomena manifest themselves via emission in various spectral bands. The clusters themselves can be used as tracers of the large scale structure. The number of clusters observable within a given volume at different cosmic epochs depends sensitively on the cosmological model. More precisely, the mean density of these objects depends both on the growth rate of structures (via the number of objects observed with mass above some cutoff) and the expansion rate of the Universe (via the volume occupied). In turn, the inhomogeneity in the distribution of clusters (their clustering) depends on cosmological parameters, with the advantage over galaxy clustering that they trace very large scales and in the linear regime. Ultimately, galaxy clusters are much closer to the concept of a "halo" of dark matter, and in principle more easily connected to theoretical predictions. For this reason they are in principle another powerful method to investigate the cosmological model. This picture is nonetheless complicated by astrophysical phenomena that occur within clusters, both in the diffuse gas that emits X-rays, and in the galaxies that live within them. Italian activity is also very intense in this field, both from the observational point of view (with large cluster surveys and detailed studies of their properties, above all from X-ray measurements) and from a theoretical point of view (with the development of important and innovative numerical simulations).

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