This volume contains a collection of articles on state-of-the-art developments in the construction of theoretical integral techniques and their application to specific problems in science and engineering. The chapters in this book are based on talks given at the Eighteenth International Conference on Integral Methods in Science and Engineering, held in Macaé, Brazil in August 2024, and are written by internationally recognized researchers. This collection will be of interest to researchers in applied mathematics, physics, and mechanical, electrical, and petroleum engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential working tool.