In this thesis, we review conformal field theory (CFT) which is a quantum field theory with conformal symmetries . T hen, by studying the bosonic string theory we see that the bosonic string theory has conformal symmetries, therefore, we are allowed to use algebra of CFT. We see that the partition function for a closed sting is equal to the free scalar partition function to the power of Twenty four. The free scalar partition function is not modular invariant unless we compactify one of dimensions of the space e, i n this situation strings emerge which have winding modes. Then, we define orbifold as a quotient space of a manifold and we investigate orbifold of a circular theory from geometric and Hilbert space view. In the following , we calculate the closed string partition function on some orbifolds of circle. First, we review the calculation of the orbifold partition function, then, we calculate the partition function for some non-abelian orbifolds of the circular theory . By calculating the orbifold partition function, we propound a supposal which is the determining of the orbifold partition function based on properties of the group representation and the ubgroups representation and w e see the soundness of our supposal by calculating and orbifolds partition functions.