  The isotropic 3-space \mathbb{I}^{3} is a real affine 3-space endowed with
the metric dx^{2}+dy^{2}. In this paper we describe Weingarten and linear
Weingarten affine translation surfaces in \mathbb{I}^{3}. Further we classify
the affine translation surfaces in \mathbb{I}^{3} that satisfy certain
equations in terms of the position vector and the Laplace operator.
