A monarchy is a form of government in which a legal person, the monarch, holds sovereign authority until death or abdication. The governing power of the monarch may vary from purely symbolic (crowned republic), to partial and restricted (constitutional monarchy), to fully autocratic (absolute monarchy).
There are elective monarchies, or as in most cases, hereditary monarchies. In hereditary monarchies, the royal family or members of the dynasty usually serve in official capacities as well. Aristocracy, despite often part of monarchies, does not inherently mean monarchic rule, class and not lifetime is its ruling oligarchic principle (e.g. maritime or aristocratic republic).
Monarchs can carry a range of titles which signal differences in authority, often multiple at a time, from king, queen, emperor, khan, caliph, tsar, sultan, to descriptions that are not exclusive to monarchs protector, autocrat, dictator, despot or tyrant.
Feudalism, which depends very much on titles as signifiers of authority, was a reacurring structure of monarchies in history, but is not a necessary structure for a monarchy. Feudal monarchies have not been the structure of contemporary monarchies or otherwise strong components of their monarchic history. Though contemporarily monarchies have been national countries, historically monarchic polities must not be understood through the logic of the nation state, since their territory and political legitimation are not necessarily understandable with a concept of nation, as for example feudal or even today in personal union monarchies are not bound to national consistancy.
A monarchy may be bound to territories and/or peoples, as in Emperor of Japan or King of Belgians.
Territorially a monarchy can be a polity in personal union, unitary or federation.
Strictly speaking is the republic the opposing form of government to a monarchy, though there have been infringements of this core principle of republics, legitimating lifetime and/or hereditary rule. Presidents are often the republican counterpiece to monarchs as heads of state.
Monarchy was the most common form of government until the 20th century. Forty-five sovereign nations in the world have monarchs acting as heads of state, sixteen of which are Commonwealth realms that recognise Queen Elizabeth II as their head of state. Most modern monarchs are constitutional monarchs, who retain a unique legal and ceremonial role, but exercise limited or no political power under the nation's constitution. In some nations, however, such as Brunei, Morocco, Oman, Qatar, Saudi Arabia, and Eswatini, the hereditary monarch has more political influence than any other single source of authority in the nation, either by tradition or by a constitutional mandate.