This proceedings book gathers papers presented at the First International Itinerant Congress on Applied Mathematics (IICAM 2025), held at the Faculty of Sciences and Techniques of Errachidia, Morocco, from October 23 to 25, 2025. As a hybrid event, it attracted researchers from North Africa, Europe, and the Middle East, with a focus on applied mathematics and modeling, differential equations and numerical methods, and mathematical contributions to computer science, particularly in artificial intelligence.The works collected in this inaugural volume are genuinely interdisciplinary, while maintaining a strong mathematical core. The book covers topics such as elliptic and fractional partial differential equations, variational methods, optimal control, mathematical programming, and data-driven learning methods.Conceived as a traveling conference that rotates among various academic institutions, IICAM is dedicated to exploring and exchanging recent advances in partial differential equations, modeling, control theory, and their diverse applications, serving as a platform for presenting cutting-edge research.