We do a systematic introduction of conformal field theory on the two-dimensional Euclidean plane, in the conformal bootstrap approach. We first explain the general ideas and techniques: the Virasoro algebra and its representations, the correlation functions and the differential equations they obey. Then we introduce and solve some of the simplest and most widely used models: Liouville theory, minimal models, free bosonic models, and, if time allows, Wess-Zumino-Witten models.