In this thesis we plan to investigate the partition function of bosonic and fermionic fields in 1+1 dimension space.so it is necessary to have prior knowledge about path integral and its relation to the partition function. Then by this relation we will calculate the partition function of different massive bosonic fields in different boundary condition . in addition conformal transformations, and Virasoro algebra will be studied in this thesis and after gathering some knowledge about supersymmetry, we will introduce the superconformal transformation and bosonization. Finally we will compare partition function of a massless bosonic field in a periodic boundary condition with a massless fermion field in an antiperiodic boundary condition on a torus and we will show that spectrum of a left moving boson is equal to spectrum of two left moving fermions.