Delve into the intricacies of two-dimensional conformal field theory in this comprehensive lecture, the fifth installment of a series. Explore advanced concepts and mathematical frameworks essential for understanding the behavior of quantum systems in two dimensions. Gain insights into the applications of CFT in string theory, statistical mechanics, and condensed matter physics. Analyze key principles, mathematical techniques, and recent developments in the field over the course of this two-hour-long academic presentation delivered by an expert in theoretical physics.