This open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress.

Tomás Chacón Rebollo is a Full Professor at the Department of Differential Equations and Numerical Analysis and the Institute of Mathematics of the University of Seville (IMUS). He is Ph.D. in Mathematics and in Numerical Analysis at the universities of Seville and Paris 6, respectively. His scientific interests are numerical and reduced-order modeling in fluid mechanics and their applications to real-world problems. He is interested in the promotion of mathematical research and transfer. He was Director of BCAM (2012-13) and IMUS (2015-19) and chairman of ICIAM-2019 Congress.

Rosa Donat is a professor at the Department of Mathematics of the University of Valencia. She has worked on numerical methods for hyperbolic conservation laws and systems and on multiresolution and subdivision frameworks that incorporate nonlinear approximation techniques. She was actively involved in the Spanish Society for Applied Mathematics (SeMA), as president in the 2016-1020 period.

Inmaculada Higueras is a full professor at the Department of Statistics, Computer Science and Mathematics of the Public University of Navarre (Pamplona, Spain). Her research focuses on time stepping methods for differential problems (ODEs, DAEs and PDEs). She has worked on numerical stability, numerical preservation of qualitative properties (positivity, monotonicity, contractivity, etc.) and on the design and implementation of robust  and efficient numerical schemes.