The fundamental theorem of affine geometry and its variants play a central role in determining order isomorphisms on classes of functions, as was also observed in the first lecture. We will discuss two other such examples. The first is that of convex functions on "windows", that is, whose domain is a convex set. The variant of the fundamental theorem is then of projective nature. We will see this is connected to the second duality discussed in lecture 1. The second example is order isomorhisms on vector spaces ordered by cones, where a new version of the fundamental theorem valid for a finite number of directions is needed. We will prove this theorem and its consequence for order isomorphisms. [Based on joint work with D. Florentin and V. Milman, and on joint work with B. Slomka]