Rousseau sets out to answer the question of whether there can be a legitimate government, and what conditions a legitimate government must meet. At the beginning of Book I, he writes:
“I mean to inquire if, in the civil order, there can be any sure and legitimate rule of administration, men being taken as they are and laws as they might be. In this inquiry I shall endeavor always to unite what right sanctions with what is prescribed by interest, in order that justice and utility may in no case be divided.”
Rousseau rejects the Hobbesian view that political authority can be concentrated in a single individual, but he has a similar view to Hobbes about the nature of sovereign authority:
“… the social order is a sacred right which is the basis of all other rights. Nevertheless, this right does not come from nature, and must therefore be founded on conventions.”
Rousseau asserts that under a legitimate government, people are as free as they would be in the state of nature. What individuals lose from the transition from the state of nature is “…natural liberty, which is bounded only by the strength of the individual. What they gain is civil liberty, which is limited by the general will.”
The general will is the collective will of the citizens. The Stanford Encyclopedia of Philosophy article on Rousseau has a helpful summary of the concept of the general will:
“Rousseau’s account of the general will is marked by unclarities and ambiguities that have attracted the interest of commentators since its first publication. The principal tension is between a democratic conception, where the general will is simply what the citizens of the state have decided together in their sovereign assembly, and an alternative interpretation where the general will is the transcendent incarnation of the citizens’ common interest that exists in abstraction from what any of them actually wants (Bertram 2012). Both views find some support in Rousseau’s texts, and both have been influential.”
Rousseau suggests that direct democracy (along the lines of ancient Athens) is better than representative democracy, though he also says that not all societies, maybe not even most, are capable of having a direct democracy. He writes in Book II, Chapter III (“Whether the General Will is Fallible”) that it would be better if voters “had no communication with one another” when they voted, an early example of a proposal for the secret ballot. In the very next sentence, he says that the general will becomes compromised when “… factions arise, and partial associations are formed at the expense of great associations.” Shades of Federalist #10 here, except that Madison is quick to point out that factions are inevitable, at least in a free society, something Rousseau seems to miss (“liberty is to faction as air is to fire” and all that). If you are reading this book, it is definitely worth reading Federalist #10 alongside Rousseau, especially since it is only five pages long.
I have not read The Social Contract before (or rather, I tried to read it and didn’t get very far). I have read the Discourse on the Origin of Inequality, years ago, so I remembered some of his ideas about moral psychology, which are not discussed as much in this book. The Social Contract can mostly stand on its own, but I recommend at least reading a quick overview of the earlier work before reading this book.