Compare and contrast the political philosophies of Hobbes and Locke.

The political philosophy of Thomas Hobbes is best seen in his work Leviathan, written amid the chaos of the English Civil War. Locke, on the other hand, laid out his political philosophy in his Two Treatises on Government, published in 1689, just after the Glorious Revolution, but written a few years earlier. Both of these authors argue that government is based on a social contract in which the people, desiring security for their property and their persons, give up some of their liberties in return for the protection afforded by government. This is not an insignificant similarity--neither author views government as based on divine right or on a paternalist family model advocated by many supporters of absolute monarchy. 

Where they differ, however, is on the type of government that would be created. Hobbes argues that to provide the order that keeps life from being "solitary, nasty, brutish, and short," government must be vested in a sovereign with absolute powers, and this government must be permanent and secure in its powers. "[N]one of his subjects," Hobbes wrote of the sovereign, "by any pretence of forfeiture, can be freed from his Subjection." The alternative was to be left in the eternal state of war, one man against every other man, that characterized the state of nature in Hobbes' mind. It is important to remember that Hobbes wrote, as mentioned above, during the English Civil War, a time of war, near-anarchy, and violence.

Locke, on the other hand, argued that the people having, out of the state of nature, agreed of their own free will to establish a government that protected their rights (he emphasized property in particular), they could and should "resume their original liberty" if that government violated the rights it was supposed to protect. So Locke essentially advocated a right of revolution that would be cited by the American Revolutionaries in particular. He also claimed that the best government was a "commonwealth" in which the people were represented, since no arbitrary government could really represent the people. For more information, see the links below. Locke's arguments about the social contract are in the Second Treatise on Government.

What are the similarities between Locke and Hobbes?

I think that one area of similarity between Locke and Hobbes is that both of them sought to articulate a relationship between the individual, their society, and their government.  Both thinkers were immersed in what could be the defining issue of the modern context.  Their examination of the condition of the human being and how this translates into political orders is of vital importance to modern political theory.  Along these lines, both thinkers articulated visions of the social contract.  This helped to explain the contours and definitions of what political society should resemble and how the individual fits into this configuration.  Both might have articulated differing visions on it, but they were both occupied with the topic of the social contract.  Finally, an interesting point about both of their lives is that they were given the same amount of pension from the British government that enabled them to continue their writing and thought.  Each thinker used the one hundred Pound pension from the government to continue their analysis and writing.