This open access book highlights the critical role of numerical software libraries in advancing applied mathematics and enabling faster, more accurate simulations in science and engineering. These libraries provide high-quality implementations of efficient algorithms, facilitating the transfer of new mathematical methods into practical applications across laboratory and industrial settings. Their importance has grown significantly in recent years, as demonstrated by the U.S. Department of Energy’s Exascale Computing Project (ECP), where libraries have helped applications adapt to cutting-edge exascale systems while improving performance on traditional architectures. The impact of these developments was underscored during the 2023 International Congress on Industrial and Applied Mathematics through a three-part minisymposium titled “Numerical Software Libraries Enabling Benefits to Scientific Applications.” These sessions showcased efforts to maximize the value of libraries, presenting examples of new algorithms and performance enhancements across diverse application areas. This volume compiles chapters based on examples presented during these sessions that illustrate the profound impact of applied mathematics on modern computational science and engineering via modern numerical software libraries.

Dr. Carol S. Woodward is a Distinguished Member of the Technical Staff in the Center for Applied Scientific Computing at Lawrence Livermore National Laboratory. She is also a Fellow of the Society for Industrial and Applied Mathematics and of the Association for Women in Mathematics.

Dr. Ulrike Meier Yang is a member of the Board of Trustees of the Society for Industrial and Applied Mathematics (SIAM) and a Fellow of SIAM.

Dr. Daniel F. Martin is a computational scientist and group leader for the Applied Numerical Algorithms Group at Lawrence Berkeley National Laboratory.