  These are notes from a mini-course about the main results of
arXiv:2206.03438: I explain how, using suitable valued fields, one obtains a
natural notion of canonical stratifications (of e.g. algebraic subsets of
$\mathbb{R}^n$). I also explain how the same techniques yield more invariants
of singularities, and I present an application to Poincar\'e series. While some
rudimentary knowledge of model theory is useful, the notes should also be
accessible without such knowledge. In particular, they contain an introduction
to the non-standard analysis needed for this approach.
