In terms of the s-wave phase shift of the two-body scattering at thermal wavelength, a systematic perturbative expansion of the Virial coefficients is developed for a two-dimensional dilute system of bosons in its gaseous phase at low temperature. The thermodynamic functions are calculated to the second order
of the expansion parameter. The observability of the universal low energy limit
of the two dimensional phase shift with a quasi-two dimensional atomic gas in
an anisotropic trap is discussed.