Popular sovereignty or the sovereignty of the people's rule is the principle that the authority of a state and its government is created and sustained by the consent of its people, through their elected representatives (Rule by the People), who are the source of all political power.
Republicanism is one possible ideology of governing a society or state as a republic. The key point is that the people hold popular sovereignty, rather than the people being subjects of a monarch. Many countries are republics, but this article covers only those that adhere to the ideology of republicanism.
Limited government is a principle of classical liberalism, free market libertarianism, and some tendencies of liberalism and conservatism in the United States. A constitutionally limited government is a system of government that is bound to certain principles of action by a state constitution.
The system of checks and balances is used to keep the government from getting too powerful in one branch. For example, the Executive Branch can veto bills from the Legislative Branch, but the Legislative Branch can override the veto.
Individual rights refer to the liberties of each individual to pursue life and goals without interference from other individuals or the government. Examples of individual rights include the right to life, liberty and the pursuit of happiness as stated in the United States Declaration of Independence.