Explore complex analysis in higher dimensions through this lecture on the Monge-Ampère equations and the Bergman kernel. Delve into the geometry of domains in Cn, Riemann's mapping theorem, and Fefferman's extension theorem. Examine Cauchy-Riemann (CR) structures, the CR version of Hartogs extension theorem, and biholomorphic geometry. Learn about the Bergman kernel and its properties through lemmas and examples. Gain insights into the L2-theory of the ∂¯-problem and its applications in complex geometry, partial differential equations, and operator theory.