This book presents a panorama about the recent progress of industrial mathematics from the point of view of both industrials and researchers. The chapters correspond to a selection of the contributions presented in the "Industry Day" and in the Minisymposium "EU - MATHS - IN: SuccessStories 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 somecollaborations between mathematicians and industrials that led to real benefits in several European companies. All the speakers were affiliated insome of the European National Networks that constitute the European Service Network of Mathematics for Industry and Innovation (EU-MATHS-IN).

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Manuel Cruz is Professor at the Instituto Superior de Engenharia do Porto and coordinator of the Mathematical Engineering Laboratory at the same institution. He was elected President of the Portuguese Mathematics Network for Industry and Innovation in 2016, and member of the European Service Network of Mathematics for Industry and Innovation executive board in 2019. He has a PhD in Applied Mathematics from the University of Porto and has participated in several challenges of technology transfer from Mathematics to Industry.

Peregrina Quintela is president of Spanish Network for Mathematics & Industry, director of the Technological Institute for Industrial Mathematics and member of the European Service Network of Mathematics for Industry and Innovation Executive Board. She holds two PhDs in Mathematical Sciences from Universidad Autónoma de Madrid and from Université Pierre et Marie Curie. She is Full Professor at Universidade de Santiago de Compostela, specialized in modelling and simulation of industrial challenges.

Carlos Parés is Professor of Applied Mathematics at the University of Málaga (Spain). He is a specialist in numerical methods for nonlinear hyperbolic systems of Partial Differential Equations. He promoted the creation and the development of the group of research EDANYA which is nowadays an international reference in the simulation of geophysical flows. He was among the promoters of the Spanish Network for Mathematics & Industry and he was member of its Managing Board from 2011 to 2019.