After a brief review of scale and conformal symmetry, we develop the basic concepts of two-dimensional conformal field theory in a top-down approach. We define primary and quasi-primary fields and the action of conformal transformations on these fields leads to the Virasoro algebra. Operator product expansions, hermitian conjugation, and the state-operator are discussed in the general setting, while results of the previous chapter are recovered as special cases. Null vectors are discussed to prepare for the later discussion of gauge transformations acting on string states. We give an overview of general results about the properties and classification of two-dimensional CFTs.