In the first part of the seminar, we will explore, through examples, three different areas of geometry that exhibit a still largely unexplored connection: affine differential geometry, pseudo-Euclidean geometry of neutral signature, and para-complex geometry. The explanation of this connection will form the basis of the second part of the seminar, where we will go into greater detail and show how it can be effectively used to address and solve certain problems that arise naturally in these settings.