REPUBLIC
You rule as the elected head of a Republican state. This state can be of any type, from a tight confederation led by a single city-state (like Ancient Rome), to a Merchant Republic (Venice), or even a confederation of more or less semi-autonomous states. There is always a major representative body, usually called a Senate, in which your decisions are debated and checked before they are implemented, and you must respect and play politics according to the tune set by the Senate and the interests lodged within it.
Due to increased individual liberties and a concern for economic productivity, commerce receives a significant boost. As a ruler bound by the Senate, you represent the sum of interests that rule your capital and your provinces, even if these interests are just oligarchic, elitist and restricted in nature at this point (eg., vote is restricted to wealthy males or just landowners). As such, citizens resent that you use your power to repress them unilaterally or impose your will over them, unlike in previous governments, so there is no military police and war weariness, while low, can become a significant problem if left unchecked.
Nonetheless, greater transparency and general freedom allow you to build research buildings that are not available before. Corruption is low, due to general satisfaction with civil liberties and also the presence of a more or less meritocratic bureaucracy, which is more efficient in dealing with administrative duties and less prone to nepotism than previously. Unit support, while average at best, can still pay the upkeep of a rather decent army, but the lack of barracks buildings means your units won’t be as well trained as in other governments.
HISTORY: The Romans, the Polish Commonwealth (Rczepospolita), the Venetians, the Carthaginians, the USA since 1787, Britain since 1647, as well as other specific civilizations with their own particularities – like Japan after the Meiji Period – can be all considered “Republics” in the game sense, as they had more or less major representative bodies that acted as a check upon and often took the role of an executive power on their own. The role of the central executive, or “ruler” was often varied, with varying and shifting amounts of power, but a “Republic” must be considered as having an essentially elitist and restricted representation first and foremost, being essentially led by the wealthy, by the landowning class or by a patrician oligarchy (as in the Carthagianian, and less so, in the Roman sense), and offering a semi-autonomous role to its provinces besides being ruled by an elected body and elected representatives.
It was not much until later in history that the concept of a government “by the people, purely for the people” emerged, with universal suffrage and a bicameral legislature.