This volume collects papers based on lectures given at the XLII Workshop on Geometric Methods in Physics, held in Bialystok, Poland in June-July 2025. These chapters provide readers an overview of cutting-edge research in quantum field theories, infinite-dimensional groups, integrable systems, noncommutative geometry, and a wide variety of other areas. Specific topics include:Twisted Araki–Woods AlgebrasMonoidal actions in Lie-algebraic contextIntroductory course to quantum formalism in low dimensionsGelfand triplets in Quantum MechanicsRiemann Hypothesis in terms of the continuous Newton flow Geometric Methods in Physics XLII are a valuable resource for mathematicians and physicists interested in recent developments at the intersection of these areas.