Explore the foundations of Drury-Arveson Space in this comprehensive 53-minute lecture from the Focus Program on Analytic Function Spaces and their Applications. Delivered by Michael Hartz from Saarland University, delve into the historical context, early papers, and the development of this important mathematical concept. Examine the process of finding the Hilbert Space, understand drivers in space, and investigate the function theoretic description. Analyze the indexing of dualism space and its noncommutative aspects. Study reproducing kernels, symmetric power series, and Fox space to gain a thorough understanding of this complex topic in mathematical analysis.