Explore the fascinating world of rational points on modular curves in this comprehensive lecture by Jan Vonk, part of the "Rational Points on Modular Curves" program at the International Centre for Theoretical Sciences. Delve into the intricate relationship between elliptic curves, modular forms, and modular curves, which are central to arithmetic geometry. Gain insights into the theoretical and computational aspects of determining K-rational points on modular curves XH(K) for various fields K and subgroups H of GL2(Z/NZ). Learn about the geometry of modular curves, their Q-rational points, and both classical and non-abelian Chabauty methods. Discover how this advanced introduction balances complex topics with practical examples, making it ideal for both experienced researchers and aspiring mathematicians in the field of arithmetic geometry.