The use of a republic goes back at least as far as ancient Akkad. The best known ancient republic was the Roman Republic, which lasted from 509 BC until 44 BC. In the Roman Republic, the principles of annuality (holding office for a term of only one year) and collegiality (holding office with at least two men at the same time) were usually observed.
In modern times, the head of state of a republic is usually formed by only one person, the president, but there are some exceptions such as Switzerland, which has a seven-member council as its head of state, called the Bundesrat, and San Marino, where the position of head of state is shared by two people.
It is rather difficult to draw a precise line between republics and monarchies. Monarchs generally reign for life, and when they die they are succeeded by a relative, either chosen by themselves or determined according to set rules. The presidents of republics, by contrast, are generally elected for a limited term, and their successors are chosen by the body that elected them. These days even non-democratic republics generally claim to be democratic, though the outcome of the election may be assured, and still maintain the ritual of regularly electing their head of state; and frequently in these states heads of states have left office voluntarily (through resignation or retirement) or been forced out (through constitutional means) by other members of the ruling elite. But there are still some exceptions -- each new Emperor of the Holy Roman Empire, for instance, was elected by the chief princes of the empire, though over the centuries the custom developed of always electing successive members of a particular family to that office. Perhaps the most significant exception among the forms of today's monarchies is, the oligarchical form of election used in the United Kingdom (described under Privy Council).
Another, older definition of the term uses the term "republic" to describe what is commonly called a representative democracy; it restricts the term "democracy" to refer only to direct democracy. See democracy for further discussion of this term usage and its history. Even this usage does not cover the many republics, past and present, that are not democratic at all (though few modern ones admit their lack of democracy).
Using this older meaning, it is said that the United States is a federal republic, not a democracy. (Although most people, including most Americans, call it a democracy, they are using the modern definition, not the older one referred to here). This usage of the term republic was particularly common around the time of the American Founding Fathers. The authors of the United States Constitution intentionally chose what they called a republic for several reasons. For one, it is impractical to collect votes from every citizen on every political issue. In theory, representatives would be more well-informed and less emotional than the general populace. Furthermore, a republic can be contrived to protect against the "tyranny of the majority." The Federalist Papers outline the idea that pure democracy is actually quite dangerous, because it allows a majority to infringe upon the rights of a minority. By forming what they called a Republic, in which representatives are chosen in many different ways (the President, House, Senate, and state officials are all elected differently), it is more difficult for a majority to control enough of the government to infringe upon a minority