We start with the actual real Analysis cambridge course. Disclaimer: Mistakes are almost surely mine and this is not official nor a recreation of what was in the lectures.
Disclaimer: I tried to keep this self contained but full proofs for many of the results from the course are in levels 4, 6.1 and 6.2.
We now have an analysis lemmas document with some more lemmas in real analysis that are fundamental to a lot of the material in levels 8.3, 8.4 and 8.5. However, this is not technically based on any Cambridge course.
We now have the complex analysis course. We see that complex functions which are merely differentiable are surprisingly elegant and the results from this course turn out to be important to the probability course (level 8.4). The fact that we need this for probability and the fact that the prerequesites from the Analysis II course have been mostly covered already on this website is the reason this is in level 8 and not later (it would otherwise be later since this is a second year course). Disclaimer: Mistakes are almost surely mine and this is not official nor a recreation of what was in the lectures.