This volume collects papers based on lectures given at the XL Workshop on Geometric Methods in Physics, held in Białowieża, Poland in July 2023. These chapters provide readers an overview of cutting-edge research in infinite-dimensional groups, integrable systems, quantum groups, Lie algebras and their generalizations and a wide variety of other areas. Specific topics include:





Yang-Baxter equation
The restricted Siegel disc and restricted Grassmannian
Geometric and deformation  quantization
Degenerate integrability
Lie algebroids and groupoids
Skew braces



Geometric Methods in Physics XL will be a valuable resource for mathematicians and physicists interested in recent developments at the intersection of these areas.