This 3rd Enlarged Edition reviews new cosmological information obtained after COBE's, WMAP's and PLANCK's observational Cosmology, as well as new data of the Hubble-Lemaitre ratio derived from type Ia Supernovae at redshifts z ≈ 1 and gravitational waves accompanying the coalescence of two neutron stars.The book preserves the lectures given by John C Mather and George F Smoot, 2006 Physics Nobel Prize Winners, at El Escorial in 1993. It also contains the work published in Acta Cosmologica (Krakow, 1998) that anticipated very accurately the dimensionless product H0t0, (Hubble-Lemaitre ratio) times ("age" of the universe). This calculation was reported by the WMAP team of NASA in 2003 and confirmed substantially by the PLANCK team of ESA in 2008.The LCDM (Lambda Cold Dark Matter) and OFL (Open Friedman-Lemaitre) solutions to Einstein Cosmological Equations -- for a massive but finite total mass/energy universe, corresponding to space curvature k ≈ 0 and k 1 and H0t0
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