The aim of this course is the study of the pullback equation. More precisely we want to find a map \(\varphi: \mathbb{R}^{n} \rightarrow \mathbb{R}^{n},\) preferably we want this map to be a diffeomorphism, that satisfies the above equation, where f, g are differential k-forms, 0 ≤ k ≤ n. Most of the time we will require these two forms to be closed.