Many political theorists and philosophers have written on the topic of the social contract. Three of the most famous and influential have been Thomas Hobbes, who wrote in the mid-seventeenth century; John Locke, who published most of his work toward the end of the seventeenth century; and Jean-Jacques Rousseau, who wrote in the mid-eighteenth century. What is interesting about these three thinkers is that their concepts of the social contract rested on very different assumptions about human nature, society, and government.
Hobbes argued in his famous work Leviathan that the natural state of man was that of a constant war. Life in the state of nature was "nasty, solitary, brutish and short." Out of self-preservation, people entered into a contract with each other, agreeing to give up essential liberty for safety. Hobbes thought the only type of government that would be able to secure peace had to be vested with more or less absolute authority, a very powerful state with prescriptive authority.
For John Locke, humans entered into society as reasonable free actors, driven to secure their property and, given his more benign view of human nature, their rights and liberties. For Locke, the point of a social contract rested in its consensual nature, and he recognized that arbitrary government was itself a threat to the rights and liberties he argued governments were instituted to protect. So Locke emphasized that the contract entailed a right to replace governments that abused their authority.
Rousseau argued in The Social Contract that the contract itself was the source of basic human rights, and indeed the development of reason itself. Indeed, it was less of an artificial construct as an expression of the inherently social nature of humans. Both Locke and Hobbes had emphasized the individualistic nature of mankind, and while Rousseau agreed with Locke that government should be consensual, he emphasized that the central problem of government was not the preservation of individual liberties, but the realization of what Rousseau called a "general will."
It should be emphasized that these are only three of many thinkers who wrote on the social contract, and that the list of political philosophers includes some relatively recent writers such as John Rawls. But these three authors have been more or less synonymous with the social contract for centuries, and the arguments presented in their books are essential to western political thought.