On Differential Rational Invariants of Finite Subgroups of Affine Group

In the case of differential field an algebraic analogue of the field of all invariant differential rational functions of surfaces relative to gauge transformations and different subgroups of affine motion group is introduced. In the case of finite subgroup of affine group it is proved that its field of invari- ant rational functions generates the above field of invariant differential rational functions as a some differential field.