A republic is a form of government in which the government is officially apportioned to the control of the people and thus a "public matter" (Latin: res publica) and where offices of state are subsequently directly or indirectly elected or appointed. In modern times, a common simplified definition of a republic is a government where the head of state is not a monarch. The word republic is derived from the Latin phrase res publica, which can be translated as "the public affair", and often used to describe a state using this form of government.

Both modern and ancient republics vary widely in their ideology and composition. In classical and medieval times the archetype of all republics was the Roman Republic, which referred to Rome in between the period when it had kings, and the periods when it had emperors. The Italian medieval and Renaissance political tradition today referred to as "civic humanism" is sometimes considered to derive directly from Roman republicans such as Sallust and Tacitus. However, Greek-influenced Roman authors, such as Polybius and Cicero, sometimes also used the term as a translation for the Greek politeia which could mean regime generally, but could also be applied to certain specific types of regime which did not exactly correspond to that of the Roman Republic. An example of this is Sparta, which had two kings but was not considered a normal monarchy as it also had ephors representing the common people. Republics were not equated with classical democracies such as Athens, but had a democratic aspect.