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The chapters correspond to a selection of the contributions presented in the \"Industry Day\" and in the Minisymposium \"EU - MATHS - IN: Success Stories of Applications of Mathematics to Industry\" organized in the framework of the International Conference ICIAM 2019 held in Valencia (Spain) on July 15-19, 2019. In the Industry Day, included for the first time in this series of Conferences, representatives of companies from different countries and several sectors presented their view about the benefits regarding the usage of mathematical tools and\/or collaboration with mathematicians. The contributions of this special session were addressed to industry people. Minisymposium contributions detailed some collaborations between mathematicians and industrials that led to real benefits in several European companies. 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