This contributed volume collects papers presented during a special session on integral methods in science and engineering at the 2023 International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE), held in Cadiz, Spain from July 3-8, 2023. Covering the applications of integral methods to scientific developments in a variety of fields, the chapters in this volume are written by well-known researchers in their respective disciplines and present new results in both pure and applied mathematics.  Each chapter shares a common methodology based on a combination of analytic and computational tools, an approach that makes this collection a valuable, multidisciplinary reference on how mathematics can be applied to various real-world processes and phenomena.