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Clusters of galaxies are the largest gravitationally bound systems in the Universe. They appear at optical wavelengths as over-densities of galaxies with respect to the field average density. In addition to the galaxies, they contain an intracluster medium (ICM) of hot (T appeq 108 K), low-density (ne appeq 10-3 cm-3) gas, detected through its luminous X-ray emission (LX appeq 1043 - 1045 erg s-1), produced by thermal bremsstrahlung radiation.

The visible galaxies and the ICM are important components of clusters, however most of the cluster mass is in dark matter. Although dark matter has not been directly observed at any wavelength and its nature remains unknown, X-ray and visible light observations provide clues to its amount and distribution in clusters.

X-ray images, starting with the Einstein satellite and continuing with ROSAT and ASCA, and now with Chandra and XMM-Newton, provide a powerful technique to trace the global cluster gravitational potential and to probe the dynamics, morphology and history of clusters. In the hierarchical scenario of the structures formation, clusters of galaxies are formed by the gravitational merger of smaller units e.g. groups and sub-clusters. Such mergers are spectacular events involving kinetic energies as large as appeq 1064 ergs. In these mergers a large portion of energy is dissipated in the ICM, generating shock, turbulence and bulk motions, and heating it. Substructure in the X-ray images as well as complex gas temperature gradients are all signatures of cluster mergers.

A significant fraction of clusters of galaxies shows the X-ray surface brightness strongly peaked at the center. This implies a high density, and cooling times of the hot ICM within the inner appeq 100 kpc of much less than the Hubble time. To maintain hydrostatic equilibrium, an inward flow may be required. X-ray observations with XMM-Newton indicate no spectral evidence for large amounts of cooling and condensing gas in the centers of galaxy clusters believed to harbour strong cooling flows. The cooling flow seems to be hindered by some mechanism, whose nature is still debated. Thus, there is no consensus on the actual existence of material "cooling" and "flowing". What is generally agreed upon is that cooling core clusters are more dynamically relaxed than non cooling core clusters, which often show evidence of cluster merger.

One of the most important results obtained with the Chandra satellite on clusters of galaxies was the discovery of sharp surface brightness discontinuities in the images of merging clusters, called "cold fronts". Initially, one might have suspected these features to be merger shocks but spectral measurements showed that these are a new kind of structure. These cold fronts are apparently contact discontinuities between the gas which was in the cool core of one of the merging sub-clusters and the surrounding intracluster gas. Cold fronts and merger shocks offer unique insights into the cluster physics, including the determination of the gas bulk velocity, its acceleration, the growth of plasma instabilities, the strength and structure of magnetic fields and the thermal conductivity.

A precise physical description of the ICM necessitates also adequate knowledge of the role of non-thermal components. The most detailed evidence for these phenomena comes from the radio observations. A number of clusters of galaxies is known to contain wide diffuse synchrotron sources (radio halos, relics and mini-halos) which have no obvious connection with the cluster galaxies, but are rather associated with the ICM. The synchrotron emission of such sources requires a population of approx GeV relativistic electrons and cluster magnetic fields on µG levels. An indirect evidence of the existence of cluster magnetic fields is also derived from studies of the Rotation Measure of radio galaxies located within or behind clusters of galaxies.

A probe of the existence of a population of relativistic electrons in the ICM is also obtained from the detection of non-thermal emission of inverse Compton origin in the hard X-ray and possibly in the extreme ultraviolet wavelengths. The combination of the observed diffuse radio and hard X-ray emissions from clusters of galaxies is used to estimate the intracluster magnetic field strengths.

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