Explore the fascinating world of complex systems in this lecture on "Quasi-crystals, Fractals, and other Beauties" by Cristiane Morais Smith. Delve into the intricacies of periodically and quasi-periodically driven complex systems as part of a comprehensive program organized by the International Centre for Theoretical Sciences. Discover the interplay between closed quantum systems with time-dependent Hamiltonians, open quantum systems, and gauge theory of coupling between matter and radiation. Learn about cutting-edge topics such as terahertz and infrared driven quantum matter, shaken optical lattices and cold atoms, Floquet time crystals, localization-delocalization physics in quasi-periodically driven systems, and dynamics of gauge theories. Gain insights into the valuable interactions between theory and experiment in these fields, and understand the importance of quantum simulation experiments in interpreting complex phenomena.