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.