In this work two major topics in Conformal Field Theory are discussed. First a detailed investigation of N=2 Superconformal theories is presented. The structure of the representations of the N=2 superconformal algebras is investigated and the character formulae are calculated. The general structure of N=2 superconformal theories is elucidated and the operator algebra of the minimal models is derived. The first minimal system is discussed in more detail. Second, applications of the conformal techniques are studied in the Ashkin-Teller model. The c = 1 as well as the c = ½ critical lines are discussed in detail.