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Explore the foundations of surreal numbers and transseries in this graduate-level lecture delivered by Alessandro Berarducci from the Università di Pisa. As part of the Fields Institute's Graduate Course on Transseries and Asymptotic Analysis, delve into the intricate world of mathematical structures that extend beyond traditional number systems. Gain insights into the theoretical underpinnings and applications of these advanced concepts, setting the stage for a deeper understanding of asymptotic analysis and its related fields.