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This lecture covers the properties and applications of carbon nanostructures, starting with the different modifications of carbon such as diamond, graphite, and fullerenes. It then delves into the discovery of carbon nanotubes, their physical and electronic structures, and their outstanding properties like high thermal conductivity and tensile strength. The synthesis methods of carbon nanostructures, including Chemical Vapor Deposition and Laser Ablation, are discussed. The lecture also explores the unique properties of graphene, such as its electrical conductivity and quantum confinement effects. Finally, it highlights the diverse applications of graphene and carbon nanotubes in electronics, energy, catalysis, and biotechnology.