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Delve into the intricacies of particle dark matter in this comprehensive lecture, exploring key concepts such as kinetic decoupling, density perturbations, and thermal distribution. Examine the collision operator and momentum transfer processes, while considering exceptions and approximations in the field. Analyze specific examples and cross-sections, and investigate the relationship between kinetic and chemical decoupling. Gain a deeper understanding of the freezing process and its implications for dark matter physics in this advanced-level presentation.