Each of these political philosophers was concerned with theorizing the best type of government. Each generally argued that the best government was one most aligned with human nature. It was on this point that they diverged, particularly Thomas Hobbes.
Hobbes argued that because mankind was naturally suspicious and greedy, governments...
were formed to keep them from a state of constant conflict. It followed, he wrote inLeviathan, that the best possible government was an absolute monarchy, unanswerable to the popular will.
Montesquieu, on the other hand, argued for a divided government, one with separation of powers between a monarch and a body dominated by nobles. He believed, more fundamentally, that governments had to be created in accordance with the particular "spirit" of a people.
Locke argued that government was based on a social contract, one in which people willingly and freely determined to submit to government. Crucially, that government had to protect the rights of individuals, or its rule could not be justified.
Rousseau, too, argued that the source of government was the consent of the governed, who entered into a social contract. His focus, though, was in establishing a government that would best express the "general will" of the people, whose will (rather than that of a single king) was sovereign over all.