Schools/education would be established by:

- Specialty organizations/guilds out of their own pocket
- Those who wish to spread knowledge/religion
- The state through taxes

If your ruler isn't bothered about bringing public education to the masses and considers knowledge/education but another tool by which to keep the poor and uneducated under heel, then they wouldn't fund a public school. Whereas guilds and specialty organizations probably have a direct control over their pupils and/or train them for a specific purpose which suits the organizations/guilds needs, or (which is more typical) it is considered more of a private school and people would have to pay to join it.