A republic (according to the most common definition used today) is a form of government (and a state where it is used) where the head of state is not a monarch.
(Another, older and less common usage uses "republic" to mean representative democracy, in contrast to "democracy" which it restricts to refer only to direct democracies. See democracy for further discussion of this usage, and its history. Below we will use the more common defintion, given at the beginning of this article.)
Most commonly in modern times the head of state of a republic has been called a President, but there are some exceptions such as Switzerland (which has a seven-member council as its head of state) or San Marino (where the position of head of state is shared by two people.)
Republics can be democratic, but they need not be. Most of the dictatorial or totalitarian states in the world today are republics, while most of the world's remaining monarchies are now democracies.
It is rather difficult to draw a precise line between republics and monarchies. Monarchs are generally rulers for life, and when they die they are suceeded 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. Even non-democratic republics, even though the outcome of the election may be assured, still maintain the ritual of regularly electing their head of state; and the 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 sucessive members of a particular family to that office.
Examples of republics include Roman Republic, Revolutionary England, the United States, France, Germany.
See also republicanism
The Rebublic is also the English term commonly used to translate Politeia, a work by Plato on his proposed ideal system of government.
Republic Aviation Company was also the name of an aircraft manufacturer. Before and during World War II they manufactured such important aircraft as the P-47 Thunderbolt and afterwards the F-84 Thunderjet.