Hello,
There are some cases where you can use an inversion ( but you can always use another alternative )
Inversion for a question : as-tu terminé tes devoirs ?
Another alternative: est-ce que tu as terminé tes devoirs ?
Inversion after an adverb as peut-être, en vain, ainsi,...: peut-être ai-je commis une erreur.
/!\ if there is a common noun or a name, you have to use this structure : adverb + common noun / name + verb + pronoun ( Sans doute Molière fut-il l’une des plus brillantes personnes de l'époque).
/!\ When you speak, you may not use it.
Stylistic inversions are very used in the literature: Les roses que bordait le vent en chœur dansaient
That's use to improve the sentence, French people love beautiful sentences !
I quoted the most used, there are others, but we don't usually find those inversions. (For example, you can find an inversion with a subject attribute : triste était Marie)