Explore the intricacies of Darmon's Program for the Generalized Fermat Equation of Signature (r,r,p) in this comprehensive lecture by Nicolas Billerey. Delivered as part of the "Rational Points on Modular Curves" program at the International Centre for Theoretical Sciences, this 1-hour 10-minute talk delves into advanced topics in arithmetic geometry. Gain insights into the study of rational points on varieties, with a focus on modular curves. Examine the theoretical and computational aspects of determining K-rational points on modular curves XH(K) for various fields and subgroups. Enhance your understanding of elliptic curves, modular forms, and their applications in number theory. Suitable for researchers and advanced students in mathematics, this lecture contributes to the broader discussion on the geometry of modular curves, Q-rational points, and Chabauty methods.