Learn about Cartan connections through the lens of exterior calculus in this advanced mathematics lecture delivered by Boris Doubrov. Explore the theoretical foundations and applications of Cartan geometry while delving into the sophisticated mathematical framework that connects differential geometry with Lie theory. Examine how exterior calculus serves as a powerful tool for understanding and working with Cartan connections, building upon fundamental concepts to develop a deeper understanding of geometric structures. This hour-long presentation serves as the second part of a comprehensive exploration of the subject, making it particularly valuable for graduate students and researchers in differential geometry, Lie theory, and related mathematical fields.