Explore a numerical approach to polylogarithms on higher-genus Riemann surfaces in this comprehensive lecture. Delve into the recent constructions of polylogarithms on higher-genus Riemann surfaces from various mathematical perspectives. Understand the importance of numerical evaluation of these functions from a particle physicist's viewpoint. Learn how to utilize the Schottky parametrization for numerically evaluating polylogarithms on a genus-two surface. Discover the application of an averaging procedure over genus-one differential forms in this process. Gain insights into the intersection of complex analysis, algebraic geometry, and particle physics through this advanced mathematical discussion.