  These are the lecture notes for a course taught at Tsinghua University in the
spring of 2022. In these notes, we develop the basic theory of vertex operator
algebras (VOAs) and their conformal blocks using complex-analytic methods. In
particular, many well-known subtleties in VOA theory (about formal variables
and, e.g., delta-functions) are presented in the form of proving the absolute
and locally uniform (a.l.u.) convergence of certain series of complex analytic
functions. We also provide many motivations from the perspective of Segal CFT.
