  The gravitational evolution of the genus and other statistics of isodensity
contours of the density field is derived analytically in a weakly nonlinear
regime using second-order perturbation theory. The effect of final smoothing in
perturbation theory on the statistics of isodensity contours is also evaluated.
The resulting analytic expression for the genus is compared with $N$-body
numerical simulations and exhibits a good agreement.
