Explore the advanced concepts of the Chabauty-Coleman-Kim Method in this fourth lecture of a series delivered by Netan Dogra at the International Centre for Theoretical Sciences. Delve into the theoretical foundations and practical applications of this method, which is crucial for studying rational points on modular curves. Learn how this technique fits into the broader context of arithmetic geometry, particularly in relation to elliptic curves and modular forms. Gain insights into the computational aspects of determining K-rational points on modular curves for various fields and subgroups. This in-depth lecture, lasting nearly two hours, is part of a comprehensive program on Rational Points on Modular Curves, designed to bridge the gap between advanced topics and concrete examples in this field of mathematics.