General solutions of the Monge-Amp\`{e}re equation in n-dimensional space

It is shown that the general solution of a homogeneous Monge-Amp\`{e}re equation in $n$-dimensional space is closely connected with the exactly (but only implicitly) integrable system \frac {\partial \xi_{j}}{\partial x_0}+\sum_{k=1}^{n-1} \xi_{k} \frac {\partial \xi_{j}}{\partial x_{k}}=0 \label{1} Using the explicit form of solution of this system it is possible to construct the general solution of the Monge-Amp\`{e}re equation.