Studies in Conformal Field Theories and Bosonization.

We describe different examples of two dimensional conformal field theories, linked by the exploitation of one of their most interesting and important features: the equivalence between bosons and fermions. The abelian version of this bosonization rule is applied in the study of the extension of the Sugawara construction for the energy-momentum tensor to the case of the superalgebra SU(M | N). Then the non-abelian version of the bosonization rule is used for the calculation of the conformal anomaly for the Wess-Zumino-Witten (WZW) model in a path-integral framework. Finally we describe "twisted bosonization", namely the correspondence between twisted WZW models and twisted free fermions. These are examples of theories containing fields with arbitrary boundary conditions which have recently been used for the description of realistic string models. The equivalence of the bosonic and fermionic theories is expressed as a consistency condition which we solve in different relevant cases.