Large Language Model (LLM) distillation, a technique for transferring knowledge from a large, powerful "teacher" model to a smaller, more efficient "student" model. It explains the core principles, including the use of soft targets generated by the teacher's probability distributions, as opposed to traditional hard labels, and the role of temperature scaling in softening these distributions to reveal more nuanced knowledge. The article details various distillation techniques, such as offline, online, and self-distillation, along with the differences between response-based and feature-based methods, before breaking down the technical mechanics of the distillation loss function and its components. Furthermore, it presents a case study using the DeepSeek model family, demonstrating how advanced reasoning capabilities are transferred through synthetic data generation and multi-stage training. Finally, the text addresses hardware infrastructure considerations for distillation, outlining VRAM requirements, GPU recommendations, and a practical roadmap for implementing a custom distillation project.