Hello! Summing up my questions and many more, I am really curious as to how monarchy works, especially in Europe. (Feel free to add about any other culture, but I am mainly interested in European history). What makes a duke more important than a count and how does one become/became one? I have a lot of questions about this, so it would be great if you could point me to a resource to learn more about this, please! Also, what is the name of the subject related to the study of nobility and royalty? I know that saying "European nobility" is really vague; it is that I just don't know much about the royalty of any specific country/period. Thank you so much!
Looks to me like you're looking for an old fashioned feudal hierarchy rundown.
The necessary condition is that the King of, say, France in the year 1050 (an arbitrary date selected by me) cannot rule all of the kingdom on his own, so he divides it among his friends. This largest (top-level, what have you) feudal subdivision is a Duchy. In France, the traditional duchies were Burgundy, Normandy, and Aquitaine (plus the Archbishop of Reims who for all intents and purposes also ruled a duchy). In England prior to the Norman Conquest, this rank was called "Earl", while in Germany, he would be called "Herzog". Further, the ruler of Brittany once annexed by France was "demoted" to the title of Duke. There are also Marquis, which are technically the same rank as Dukes but rule border territories. Thus they have more responsibilities, but also more rights (this title is also present in Germany as "Magrave").
In turn, a Duke in the year 1050 in turn cannot conceivably rule his entire Duchy on his own, so he splits up the territory among his friends. This second subdivision is called a Country, ruled by a Count or Viscount. The Duke of Normandy, for example, split up his Duchy in the counties of Rouen, Meulan, Evereux, Eu, Contentin, Cau, Bayeux, Avranche, Aumale, and Alençon. The Counts, in turn, would split up their counties among Barons. Below Barons were Knights, who would be given just enough land and serfs to maintain arms, armor and a stable (not that Barons and Counts wouldn't fight as knights in time of war; the terminology gets messy fast).
Some counties (like the County of Toulouse) didn't belong to a Duchy, and were directly under the rule of the King (and in the case of Toulouse, the King later ruled it directly as his own possession from the thirteenth century on). Further, several Counts under the direct rule of the King who had either by purchasing or marrying (or even war) acquired large, near-Duchy sized territories were elevated by the King to the rank of Duke (Bourbon, Orleans, Anjou, Berry, Angoulême, Alençon, Touraine).
After about the 15th century, the land-title relationship began to break down, although the hierarchy continued to exist. Sometimes when a noble title was created the overlord gave land and/or a house with it, sometimes they did not. Sometimes the family sold or lost the land, but kept the title.
So in brief, here's the hierarchy:
King
Duke/Marquis
Count
Baron
Knight
Of course, these neat little boxes are problematic. I think they're a very useful framework, but some people really don't like the way it ties you down.