After using the Oghma Infinium (I selected the Path of Magic) illusion training isn't advancing my skill level nor advancing my progress to the next level. Training other skills seems to work fine.

Illusion isn't maxed out, doing the training still takes my gold and still counts as one of the five trainings per level, but it won't advance the actual skill level. Any suggestions?

Welcome to the forums

Have you got any mods that change the magic system ?

Does casting illusion spells still work normally to improve the skill levels ?

Are you running the latest patch and/or verified the cache ?