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The basic relations between the luminosity distance, the matter density $\Omega_M$, and the cosmological constant $\Omega_{\Lambda}$ are derived. The universal character of the luminosity of SN1a is described, and the experimental status of the determinations of the Hubble constant, $\Omega_M$, and $\Omega_{\Lambda}$ are recalled. The large supernovae surveys foreseen in the near future, and their expected performances are reviewed. Some aspects of the supernovae explosions are briefly summarised
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