  A dilute two-dimensional (2D) Bose gas at zero temperature is studied by the
method developed earlier by the authors. Low density expansions are derived for
the chemical potential, ground state energy, kinetic and interaction energies.
The expansion parameter is found to be a dimensionless in-medium scattering
amplitude u obeying the equation 1/u+\ln u=-\ln(na^2\pi)-2\gamma, where na^2
and \gamma are the gas parameter and the Euler constant, respectively. It is
shown that the ground state energy is mostly kinetic in the low density limit;
this result does not depend on a specific form of the pairwise interaction
potential, contrary to 3D case. A new form of 2D Gross-Pitaevskii equation is
proposed within our scheme.
