First and foremost, the medieval monarch had to work on staying alive, because there were any number of other people out there who might want the throne and be willing to do what it took to throw him out.
Many monarchs were almost obsessed with the idea of producing an heir who could provide their countries with stability when they died.
The strong desire to produce an heir shows that most monarchs were genuinely interested in providing their countries with stable governments. Having a number of mistresses was also an object for a lot of monarchs, but never had the importance of legitimate heirs.
Some monarchs were powerfully motivated to enlarge the areas they controlled. Some of these were among the greatest.
Some monarchs were very interested in the well being of their subjects, and worked hard at improving education, care for sick people, and charity for the poor. There were kings and queens who were recorded to have given food to poor people every day before they had breakfast themselves.
Some monarchs were very interested in promoting trade and crafts.
There were a few sadists who just wanted to make life miserable. Fortunately, there seem not to have been many.
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The monarchs of Europe believed that they were divinely chosen.
It made the Church dependent on individual monarchs.
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Finding riches.
Mercantile was the primary occupation along with farming during the the Middle Ages.