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While I find the question borderline, I succumb to the temptation to answer.

Knot Theory: Kawaii examples for topological machines.

Topology is full of big machines, which may seem rather daunting to the student. But knot theory is a wonderful playground for toy models of many of these machines, where you can see how they work and visualize what they are doing. And one can draw pictures.
I think that a collection of these examples would be useful to students (I would have loved to have had it) or to people who would like to teach topology. And I don't think anything like this exists, really. The machine itself would be introduced only briefly, refering to somewhere else for more detail, while the knot theory example would be fleshed out in full.
For example, curvature of knots is the perfect playground for the Gauss-Bonnet Theorem. Computations of homology in knot theory give perfect toy examples (with pictures you can draw) for Meyer-VietorisMayer-Vietoris, the snake lemma, and other homological arguments. Ideas such as localization and Brown representability come up naturally. And an Alexander module gives a perfect playground for commutative algebra over a UFD.
So the idea would be to give sophisticated proofs of simple facts, letting the topological machines play the lead rollrole. The student of topological machine X might then read the book by looking up the relevant section, which would give a kawaii (cute?) example in knot theory, highlighting how exactly the machine is working, and shedding light on its nature.
How likely am I to write it? I've toyed with the idea for a long time. For the book to be useful, it needs to be very visual and pedagogical, to make it light fluffy reading for one who knows the machine, and educational reading for one who doesn't. And becaue I have high asprations for it, it may take a while. But I do have intentions of actually writing it at some point, even if I don't yet know when that might be.