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Type Ia Supernovae and the discovery of the Cosmic Acceleration

I present a review of the research and analysis paths that converged to make Type Ia SNe the most mature cosmological distance estimator of the present time. The narrative starts with the first works in the early decades of the 20th century and finishes with the more recent results. The review was written by a member of the High Z Supernova Search Team, the international group of astronomers that discovered Cosmic Acceleration in 1998. This result, confirmed by the Supernova Cosmology Project in 1999, received an impressive string of recognition culminating with the current Nobel prize in Physics. The review is presented thinking of physicists with a strong interest in Cosmology, who might have pondered why was that, after decades of not being able to agree upon the rate of cosmic expansion, astronomers were so quick to concur on cosmic acceleration.