This work covers various topics in modern Theoretical Physics, in the attempt of describing our world. In particular, the subject of String Theory and related fields are considered. Two-dimensional Conformal Field Theories play a crucial role in the construction of realistic four-dimensional string models. Results in CFT's have a broader validity since their range of applications goes beyond String Theory. Here new CFT results are given, for a particular class of theories (namely the permutation orbifold), and then used in the context of string model building.