Computational Mathematics Driven by Industrial Problems : Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Martina Franca Italy June 21–27 1999 These lecture notes by very authoritative scientists survey recent advances of mathematics driven by industrial application showing not only how mathematics is applied to industry but also how mathematics has drawn benefit from interaction with real word problems.The famous David Report underlines that innovative high technology depends crucially for its development on innovation in mathematics. The speakers include three recent presidents of ECMI one of ECCOMAS (in Europe) and the president of SIAM