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This lecture covers the concept of quantum numbers related to the electron's angular momentum quantization, the introduction of the spin as a fourth quantum number, and the experimental evidence supporting the existence of the electron's spin. It explains how the spin of the electron generates a magnetic moment, the implications of the spin in the hydrogen atom, and the abnormal magnetic moment due to the electron's interaction with the vacuum's electromagnetic field. The lecture also delves into the mathematical structure of the electron's spin, its relation to the angular momentum, and the necessity of incorporating relativity in quantum physics to properly describe the electron's spin.