What exactly is The Royal Ballet?
It is a ballet company at the Royal Opera House. It is located in London, England.
Do they teach ballet or is it merely the site where ballets are performed?  Or is it a combination of the two?
They have a school specifically for teaching them called the Royal Ballet School.
That is very cool.  I assume that they are very well-known?  Personally, I know nothing about ballet.
I think they are pretty well-known. They house about 100 dancers.
Do you know the statistics of the dancers?  All men, all women?  50% of each; etc.?
No I do not unfortunately. The Prima ballerina is Dame Margot Fonteyn though.
What interesting facts make her the prima ballerina?
Prima ballerina assoluta
Prima ballerina assoluta is a title awarded to the most notable of female ballet dancers. To be recognised as a "prima ballerina assoluta" is a rare honour, traditionally reserved only for the most exceptional dancers of their generation. Originally inspired by the Italian ballet masters of the early Romantic ballet, and literally meaning "absolute first ballerina", the title was bestowed on a prima ballerina who was considered to be exceptionally talented, above the standard of other leading ballerinas. The title is very rarely used today
of London (later the Royal Ballet) who still almost religiously perform many of these ballets with little changes from when they were first staged. It was through these revivals by Sergeyev in London with aid of these notations that the ballets of Petipa where first staged in the west, forming the nucleus of what is now known as the Classical Ballet repertory for not only the ballet of England but for the world.
In 1969 the Harvard University Library purchased the collection, which is today known as the Sergeyev Collection. The collection