Notes on translating solitons for Mean Curvature Flow

The purpose of these notes is to provide an introduction to those who want to learn more about translating solitons for the mean curvature flow in ${\mathbb{R}}^3$, particularly those which are complete graphs over domains in ${\mathbb{R}}^2$. In this paper we describe a full classification of complete translating graphs in ${\mathbb{R}}^3$.