amindumi

This is the showpiece. If you want one word to demonstrate what Esperanto's affix system actually does, amindumi is it, and the decomposition is a gift: am- (love) plus -ind- (worthy of) plus -um- (the wildcard) plus the verb ending. Take it in pieces and you get aminda, lovable, worthy of love, and then -um- verbs it into doing something in the general neighbourhood of lovability. Worthy-of-love-ing. Which is, when you look at what courtship consists of, an almost embarrassingly exact description: you are not loving them, you are making a case that you are worth loving.

-Um- is the affix Zamenhof left deliberately empty. It carries no fixed meaning, by design, and it is what the language reaches for when a word obviously belongs to a root but no regular suffix says how. That is why amindumi has to be learned rather than computed: the parts tell you the neighbourhood, a century of use picked the house. The -um wildcard sets out the rest of the family, plenumi and kolumo and brakumi and the ones that catch people out.

In use it is transitive and the object is the person: li amindumas ŝin. It sits at the formal, slightly old-fashioned end of the register, exactly like English woo and court, and that is part of its charm rather than a problem. For the light modern sense you want flirti. For the outcome you want edziĝi. Amindumanto is a suitor, and it is one of the few nouns in any language that tells you exactly what its owner is up to.