I will review the basic principles of two-dimensional conformal field theory, and some important results. First I will explain the origin and consequences of the existence of a Virasoro symmetry algebra. Then I will sketch the conformal boostrap approach to conformal field theory. Finally I will introduce minimal models and Liouville theory, and sketch how their spectrums and correlation functions can be computed exactly.
(Based on https://arxiv.org/abs/1609.09523 )