Explore the fascinating world of random matrices and Dyson-Schwinger equations in this comprehensive lecture by Alice Guionnet from ENS, Lyon, France. Delve into key concepts such as matrix models, the MGK central equation, and integration by parts. Gain a deep understanding of how these equations are derived and their unique solutions. Learn about expectations and the importance of these mathematical tools in various applications. This talk, part of the School and Workshop on Random Matrix Theory and Point Processes, offers valuable insights for mathematicians and researchers interested in advanced probability theory and its intersections with physics.