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I present a summary of the four lectures given on these topics: (i) Galaxy Clusters in a cosmological context: an introduction; (ii) Galaxy Clusters in X-ray: how and what we observe, limits and prospects; (iii) X-ray Galaxy Clusters and Cosmology: total mass, gas mass & systematics; (iv) Properties of the ICM: scaling laws and metallicity. [ABSTRACT FROM AUTHOR]

Deep X-ray surveys have shown that the cosmic X-ray background (XRB) is largely due to the accretion onto supermassive black holes, integrated over the cosmic time. These surveys have resolved more than 80% of the 0.1-10 keV X-ray background into discrete sources. Optical spectroscopic identifications show that the sources producing the bulk of the X-ray background are a mixture of obscured (type-1) and unobscured (type-2) AGNs, as predicted by the XRB population synthesis models. A class of highly luminous type-2 AGN, so called QSO-2s, has been detected in the deepest Chandra and XMM-Newton surveys. The new Chandra AGN redshift distribution peaks at much lower redshifts (z ≈ 0.7) than that based on ROSAT data, indicating that Seyfert galaxies peak at significantly lower redshifts than QSOs. [ABSTRACT FROM AUTHOR]

The ROSAT Deep Surveys in the Lockman Hole have revealed that AGNs are the main contributors (∼75 %) to the soft X-ray background in the 1-2 keV band. Using new optical/infrared and radio observations we have obtained a nearly complete identification (93 %) of the 91 X-ray sources down to a limiting flux of 1.2 · 10[sup -15] erg cm[sup -2] s[sup -1] in the 0.5-2.0 keV band. We present the optical colours and the emission line properties of our AGNs in comparison with other X-ray selected AGN samples. Furthermore we discuss the fraction of red AGNs found in the ROSAT Deep Surveys. From the ROSAT Deep Surveys we see no evidence for a new class of X-ray bright galaxies, which significantly contributes to the soft X-ray background. [ABSTRACT FROM AUTHOR]