Explore the foundations of lattice-based cryptography in this Richard M. Karp Distinguished Lecture by Daniele Micciancio from UC San Diego. Delve into the mathematical problems on point lattices that form the basis of modern cryptographic functions. Discover how these lattice-based systems offer resistance against quantum adversaries and enable computations on encrypted data. Learn about the evolution from subset-sum and knapsack problems to lattice problems, and understand key concepts like Learning With Errors (LWE) encryption. Examine the development of Fully Homomorphic Encryption (FHE), including homomorphic addition, multiplication, and bootstrapping techniques. Gain insights into the geometric aspects of lattices, public key encryption methods, and the timeline of FHE advancements. This comprehensive lecture provides a thorough overview of lattice-based cryptography, its theoretical foundations, and its potential applications in post-quantum security and homomorphic encryption.