Explore the fascinating world of Faraday waves in this comprehensive lecture by Laurette Tuckerman from Sorbonne University. Delve into the history, theory, and numerical simulations of the Faraday instability, where standing waves appear on the free surface of a vertically vibrated fluid layer. Discover exotic patterns such as quasipatterns, superlattices, and quasi-hexagons alternating with beaded stripes. Learn about the Benjamin & Ursell inviscid linear stability analysis, viscous stability analysis, and full nonlinear simulations using high-performance computing. Examine the long-time evolution of hexagonal patterns, Fourier spectra, and the intriguing behavior of Faraday super-squares. Investigate the application of these concepts to spherical interfaces and explore predictions from symmetry theory. Gain insights into cutting-edge research on hydrodynamic instabilities and pattern formation in fluid dynamics.