Explore the intricacies of lattice-based cryptography in this invited talk at PKC 2010 by Daniele Micciancio. Delve into the fundamental concepts of duality and its applications in cryptographic systems. Learn about the underlying principles, including the reasons behind their effectiveness, and gain insights into the skin and syntax of lattice-based structures. Engage in practical exercises to enhance understanding, focusing on decoding techniques and their relevance to cryptography. Examine real-world examples and discover the process of public key generation in lattice-based systems. Investigate the GBV (Gentry-Brakerski-Vaikuntanathan) crypto system, a significant development in this field. This comprehensive lecture provides a solid foundation for researchers and cryptography enthusiasts interested in advanced lattice-based security methods.