The work of Thomas Hobbes is about as poorly understood as that of Niccolò Machiavelli in the popular imagination, not least because we stand so far removed from the circumstances which begat it. What Hobbes shares in common with Old Nick is a rejection of the concern held by classical philosophy of how men ought to live, and an investigation into how they actually do live; this latter topic is the subject of The Prince, and it is the subject of Hobbes' Leviathan. Seen in this light, these two are the founders of political science as understood in the modern sense.
Machiavelli was mostly concerned with the exception, extreme situations which are encompassed in the term coup d'etat in its broadest sense.1 But Hobbes instead went about an investigation into what were the origins of civil society and politics on the basis of an investigation into what man is. This was a much broader venture than Machiavelli undertook systematically, and was supposed to apply to all societies everywhere; it was hence a form of natural law teaching, in that it sought the origins of the just actual law in human nature.
Hobbes' ideas on why societies are formed were very different to those of the classics. According to Aristotle and Plato, man is naturally a social creature and this drives him to form civil societies, which can broadly be said to exist for the perfection of virtue. But for Hobbes, man is naturally anti-social - he does not by nature love his life amongst the world of men, but hates and fears it. This is because for Hobbes, the most fundamental driving passion in every person is the fear of violent death; a death which can be inflicted on anyone at any time in the state of nature which exists prior to any human society. No-one desires death, but even the strongest can be overcome by a temporary alliance of the weak.
In Hobbes' view, there is only one inalienable natural right: the right to self-preservation which is inherent in the strongest and most fundamental human desire, which is the desire for the same. In the state of nature, every human is legitimately allowed to employ any means towards this end, up to and including the destruction of any other human. This is because Hobbes derives the rights from necessity - from the Is - and not from the Ought, as the classical philosophers did. Life in the state of nature, famously called by Hobbes the "war of all against all", results in a human condition which he - even more famously - called "solitary, poor, nasty, brutish and short".
There are two reasons for this. The first is the essential scarcity of things in the world, meaning that people must compete with one another for the things necessary for living at all (nevermind for pleasurable living). Secondly, there exists in the state of nature what international relations scholars nowadays call a security dilemma. This is a term used to describe why, in the view of some such scholars, war is an inevitable part of the international system even if no state actually desires it. In Hobbes' system, the security dilemma consists in the problem that individuals share vulnerability to violent death at the hands of others, and are never able to have perfect knowledge of the intentions of these others. Anxiety multiplied by uncertainty almost always results in an exaggeration of the scale of the threat, as history has repeatedly shown.
So far this all sounds like a jolly depressing view of human nature. But this is all about the state of nature, not the state of civil society; much less is it about how Hobbes thinks the perfect civil society should be run! Hobbes maintains that to solve the inherent problem of human living-together outlined above, men form a civil society. The Leviathan has often been criticized because it is supposed by a casual reading of Hobbes' work that he views the perfect civil society as a totalitarian dictatorship, in which men dispense with all liberty so that they might enjoy unlimited security. Yet nothing could be further from the truth.
Hobbes' philosophy is grounded ultimately not in duties, but in rights. The function of Hobbes' state is the mere protection of these rights. It can be argued that this makes Thomas Hobbes the founder of classical liberalism, and it is why his name is invoked in the same breath as the foundation of the United States of America. A perfect tyranny demands of men that they relinquish all rights and accept only duties. Yet a participant in Hobbes' state is required to surrender only so much of his natural right to the sovereign that it can maintain the public peace, and no more. It means essentially an agreement between men that they will not harm one another, and will remain cohesive when their society is threatened from the outside; all other rights they retain. Jesus of Nazareth said to man that he ought to "Do unto others as you would have others do unto you," whereas Thomas Hobbes said "Do not that to another, which thou wouldst not have done to thyself." The difference is obvious; the first speaks of duties, the second of rights.
Men enter into such an agreement because they most of all desire to avoid violent death, and it is the establishment of a peaceful commonwealth that allows them to do so. Once this commonwealth has been established, man is free to exercise his other passions and desires, which Hobbes identified with the seeking of pleasure and the avoidance of pain. Morality within such a society consists in the habit of keeping one's agreements with fellow men, and of nothing more; and the most fundamental agreement is the social contract itself, which is the agreement not to do others harm. Hobbes is then truly the first philosophical exponent of the small state, which the Victorians called the "nightwatchman state". He was not the first totalitarian philosopher, but the first bourgeois philosopher.
1. The Oxford English Dictionary provides the best definition: "a sudden and decisive stroke of state policy; spec. a sudden and great change in the government carried out violently or illegally by the ruling power". See coup d'etat for more details; also raison d'etat.