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This lecture by the instructor covers the synthesis of nanocrystals through top-down and bottom-up approaches, focusing on the nucleation and growth mechanisms. It delves into classical and non-classical nucleation theories, discussing the role of monomers, nuclei, and nanocrystals. The lecture explores the factors influencing nucleation rates, such as saturation and temperature, and the size distribution of nanocrystals. Additionally, it explains the chemical reaction mechanisms involved in the synthesis of metal oxides and semiconductors, highlighting the importance of sol-gel reactions and thermal decomposition. In-situ studies using transmission electron microscopy and infrared spectroscopy are presented to corroborate the non-classical growth of nanocrystals.