ABSTRACT: These lectures are complementary to the introduction to Conformal Field Theory given recently by Marina Huerta. Their goal is to show how main ideas and mathematical structures of the formal CFT approach show up in a simple and well-known example -- the 2D Gaussian model (free massless boson). We will also consider a typical deformation of this theory, the 2D sine-Gordon model, that displays a topological (Berezinskii-Kosterlitz-Thouless) transition. Questions related to fermion-boson democracy will be finally discussed.