Explore the groundbreaking Atiyah Singer Index Theorem in this distinguished lecture by renowned mathematician Madabusi Raghunathan. Delve into the intersection of Differential Equations, Differential Geometry, and Topology as the speaker provides an overview of this monumental 20th-century mathematical achievement. Gain insights into the theorem's formulation, historical context, and its significance across multiple mathematical disciplines. While some familiarity with smooth manifolds and vector bundles is beneficial, the lecture aims to introduce key concepts, making it accessible to those not specializing in these areas. Learn from Professor Raghunathan, a leading mathematician known for his contributions to discrete subgroups of Lie groups, as he shares his expertise on this profound theorem that has shaped modern mathematics.