Complex sentence: Up until the late medieval period, the majority of schools were controlled by the church, or restricted to the sons of members of guilds, trades or livery companies, for example the Merchant Taylors' School.
Split into simpler sentences: Up until the late medieval period, the majority of schools were controlled by the church and had specific entrance criteria. Others were restricted to the sons of members of guilds, trades or livery companies, for example the Merchant Taylors' School.