someone who is in charge of a school [= headteacher British English]
school[countable] American EnglishSE
a small school with just three teachers and the principal
someone who is in charge of a university or college
university/collegeSE [countable] British English
the main person in a business or organization, who can make important business decisions and is legally responsible for them:
business[countable] American English
The principal of the business has an office in New York.
the main performer in a play or in a group of musicians, dancers etc:
She later became a principal with the Royal Ballet.
the original amount of money that is lent to someone, not including any of the interest