Explore the advanced concepts of the Chabauty-Coleman-Kim Method in this comprehensive lecture, the second in a series delivered by Netan Dogra at the International Centre for Theoretical Sciences. Delve into the theoretical foundations and practical applications of this powerful technique used in arithmetic geometry to study rational points on modular curves. Gain insights into the geometry of modular curves, their Q-rational points, and both classical and non-abelian Chabauty methods. Learn about the computational aspects involved in determining K-rational points on modular curves XH(K) for various fields and subgroups. This nearly two-hour lecture is part of a broader program on Rational Points on Modular Curves, designed to bridge advanced topics with concrete examples and foster collaboration among experts in the field.