Explore the advanced mathematical concepts of Classical and Quadratic Chabauty methods in this second lecture by Samuel Le Fourn, part of the "Rational Points on Modular Curves" program. Delve into the intricate world of arithmetic geometry, focusing on techniques used to determine and describe rational points on varieties, particularly modular curves. Gain insights into the geometry of modular curves, their Q-rational points, and non-abelian Chabauty methods. Benefit from a balanced approach that combines advanced topics with practical examples, making it suitable for both experienced researchers and aspiring mathematicians in the field of number theory and algebraic geometry.