Conformal field theory (CFT) is a quantum field theory with conformal symmetries. In this thesis, at first we introduce two-dimensional CFT and review Virasoro algebra as the symmetry algebra of this theory. We calculate the partition function of massless free fermions and free bosons as simple CFTs. Conformal field theory on the torus is modular invariant. As an example, the partition function of bosonic field is equivalent to partition function of two Dirac fermions, if we assume bosonic field compactified on a circle of definite radius. We will study bosonic string theory as a conformal field theory, and review BRST quantization of closed bosonic strings. The action of a string moving on a group manifold is given in terms of the field g which takes value in some Lie group G . In this theory the current algebra satisfy affine Kac-Moody algebra which contains a character known as level of the current algebra. The action of this theory is the WZW action. We consider gauging of WZW models by a subgroup of the symmetry group as observables take value in the Lie algebra of this subgroup. Using Sugawara construction, one can show that critical level of algebra is equivalent to the tensionless limit of bosonic string. The effective action describes, in the tensionless limit, the geometry of target space reduces to one-dimension and gravity decouple from the spectrum in the form of a Liouville field with given background charge and zero cosmological constant. Keywords: Conformal Field Theory, Virasoro Algebra, Bosonic String, Affine Kac-Moody Algebra, Sugawara Construction, WZW Action, Tensionless Limit, Liouville Field .