  The partition function of a two-dimensional quantum gauge theory in the
large-$N$ limit is expressed as the functional integral over some scalar field.
The large-$N$ saddle point equation is presented and solved. The free energy is
calculated as the function of the area and of the Euler characteristic. There
is no non-trivial saddle point at genus $g>0$. The existence of a non-trivial
saddle point is closely related to the weak coupling behavior of the theory.
Possible applications of the method to higher dimensions are briefly discussed.
