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André Weil (Paris 1906 -Princeton 1998) has a name whose fame extends beyond the circle of mathematicians. For all those who are not close to mathematics, Weil is the name of his sister Simone, the philosopher who died in tragic circumstances in Ashford (England) in 1943. André, an intellectual of vast culture, speaking and reading Sanskrit, lived at a young age in India, in order to set up a mathematics department. He fled France at the time of the occupation to gain a foothold in the United States and never returned to settle in France, his country of birth and education, where, in particular, he had co-founded the Bourbaki group. André Weil is one of the founding fathers of what we call Arithmetic Geometry. The text we are going to discuss has profoundly influenced arithmetic and algebraic geometry since its publication. Conference of the cycle "A text, a mathematician" of the Mathematical Society of France. January 15, 2014 at the National Library of France.