Explore the fascinating world of Rademacher sums in this comprehensive lecture on the asymptotics of optimal constants in the Khinchine-Kahane inequality. Delve into the history and significance of Rademacher systems, consisting of independent symmetric +/-1 random variables, and their applications in both real and vector-valued scenarios. Examine classical moment inequalities for Rademacher sums, tracing their origins from Khinchine's work in 1923 to Kahane's contributions in 1964. Gain insights into recent developments in the field and understand the importance of these mathematical concepts that have been studied for over a century.