Royal dukedoms in the United Kingdom
In the British peerage, a royal duke is a member of the British royal family, entitled to the titular dignity of prince and the style of "His Royal Highness" who holds a dukedom. Dukedoms are the highest titles in the British roll of peerage and the holders of these particular dukedoms are Princes of the Blood Royal. The holders of the dukedoms are royal not the titles themselves. They are titles created and bestowed on legitimate sons and male-line grandsons of the British monarch, usually upon reaching their majority or marriage. The titles can be inherited but cease to be called "royal" once they pass beyond the grandsons of a monarch. As with any peerage, once the title becomes extinct, it may subsequently be recreated by the reigning monarch at any time.
Forms of address in the United Kingdom
"Eldest sons of dukes, marquesses and earls use their father's most senior subsidiary title as courtesy titles: note the absence of "The" before the title. If applicable, eldest sons of courtesy marquesses or courtesy earls also use a subsidiary title from their (great) grandfather, which is lower ranking than the one used by their father. Eldest daughters do not have courtesy titles; all courtesy peeresses are wives of courtesy peers."
"(Heirs-apparent and heirs-presumptive of Scottish peers use the titles "Master" and "Mistress"; these are substantive, not courtesy titles. If, however, the individual is the eldest son of a Duke, Marquess or Earl, then he uses the appropriate courtesy title, as noted above.)"