Explain Hobbes’s idea of the social contract. In what context did he write the Leviathan?

In Leviathan, Hobbes presents us with an imaginative reconstruction of what life must have been like before the first civil society was founded. Simply put, it was horrible. Without any law or any government or rules, complete anarchy reigned. Everyone was involved in a constant war of "all against all." No one could feel safe in such a brutal environment; an individual's property or person was in danger of being taken by anyone else at any time. The law of the jungle prevailed, meaning that no one had sufficient security to be able to engage in the kind of activities that characterize life in modern societies, such as trade, commerce, science, and the arts. In the state of nature, life was, in the words of Hobbes, "solitary, poor, nasty, brutish, and short." In other words, humans were reduced to the status of animals.
But they were still rational animals, nonetheless. Because they were rational, human beings realized that such a state of chaos could not be allowed to continue. In order to protect their lives and property, they got together to form a civil society in which they gave up their natural rights and invested absolute power in a sovereign ruler. As part of this agreement, the sovereign would keep the peace, enforce legal contracts through the courts, and maintain law and order. In return, his subjects would give him absolute obedience at all times.
Most versions of social contract theory emphasize the protection of individual rights. Yet Hobbes's theory is different because, under his theory, citizens actually give up their rights to a sovereign in return for peace, order, and stability. In Hobbes's political philosophy, the sovereign is the only one who still lives in a state of nature; as we saw earlier, in a state of nature, people can do whatever they want. It remains the case with the sovereign. According to Hobbes, the sovereign has the absolute right to command obedience at all times because, unlike his subjects, he has not given up his natural rights as part of the social contract.
Hobbes lived through a period of great political turmoil during which Britain was riven by conflict. The English Civil War caused great division and bloodshed between the Royalist supporters of King Charles I and their Parliamentarian opponents. Hobbes himself was forced to flee the country during these troubled times, and his personal experiences of the anarchy and disorder both during the Civil War and after it strongly influenced the content of Leviathan and all his other political works. Hobbes wanted to see the establishment of an authoritarian system of government in order to prevent the kind of disorder and violence that had torn his native country in two and turned his life upside down.