Parts One and Two of this essay can be read here and here respectively.
It may seem ironic that the State is the last, and perhaps least, important filter through which we will be looking at something called The Republic. This anomaly has more to do with the part of that work under examination as the full task of constructing this ideal society actually begins in Book Three. That is not to say however that ideas about the State do not figure into the dialogues of Books One and Two. There are several ideas about the State that surface before the focus of the dialogue as a whole turns specifically to it.
The first inquiry into the nature of Justice (begun by Cephalus and then defended by Polemarchus) concerns itself with the ways in which a person may be just. The second one, born from Thrasymachus’ argument that Justice is merely a euphemism for the stronger exerting their will over the weaker, turns its attention almost immediately to the broader expression as it relates to the way that humanity rules itself. After establishing that there are different forms of government (tyrannies, democracies, and aristocracies listed in particular), Thrasymachus provides us with our first description of the State and its function.
...the different forms of government make laws democratical, aristocratical, tyrannical, with a view to their several interests; and these laws, which are made by them for their own interests, are the justice which they deliver to their subjects, and him who transgresses them they punish as a breaker of the law and unjust. And that is what I mean when I say that in all states there is the same principle of justice, which is the interest of the government; and as the government must be supposed to have power, the only reasonable conclusion is, that everywhere there is one principle of justice, which is the interest of the stronger. 
What we find in Socrates’ examination of his claims, however, is a curious tendency of any conversation about States as a whole degenerating into a conversation about the particular ruler or rulers that govern that state. The dialogue, begun as an inquiry into the just action of a person, first references the State as the arbiter of the punishment due to that person should they behave in a criminal manner.
Socrates begins his rebuttal to the argument by asking Thrasymachus if he believes that “it is just for subjects to obey their rulers” . Each of the three types of government being considered (aristocratic oligarchy, tyranny, and democracy) employs its own mechanisms for first crafting those laws and then enforcing them. It is also worth noting that other types of governance like imperial, monarchical, or theocratic (all extant prior to, during, and after the classical Greek civilizations rose and fell) are not considered. Regardless of the type of government under consideration, the actual act of creating, enforcing, and obeying or not obeying the Law is strictly a matter of human behavior. The State, in this sense, is not a person and so while it may be said to foster or stifle Justice, the success or failure of this effort is to be found not in abstractions, but in human behavior.
The issue of the State is largely ignored until mid-way through the second book as Socrates begins his rebuttal to Glaucon and Adeimantes’ lengthy defense of injustice as an value widely praised by gods and men alike. After raising again the idea that Justice may be thought of as both a human virtue as well one related to the State, Socrates argues that, as the State presents a wider-range of concerns that of a single human being, it makes sense to consider Justice first as virtue of a State and then draw analogies from the greater to the lesser. He then lays out his plainest argument for the existence of the State, suggesting that it arises, “out of the needs of mankind; no one is self-sufficing, but all of us have many wants.” .
The following paragraphs are a careful construction of the various facets of the population of a State, based on the aforementioned premise that all complexity arises from human want. After demonstrating that merely providing for the basic staples of human existence (food, clothing, shelter) gives rise to a surprisingly diverse population, Glaucon suggests that a truly civilized state would also include as many luxuries and entertainment as its population could support which, again, adds whole new classes and subsets of laborers. This concession leads Socrates to a startling conclusion.
SOCRATES: Then we must enlarge our borders; for the original healthy State is no longer sufficient. Now will the city have to fill and swell with a multitude of callings which are not required by any natural want…And the country which was enough to support the original inhabitants will be too small not and not enough?
GLAUCON: Quite true.
SOCRATES: Then a slice of our neighbors’ land will be wanted by us for pasture and tillage, and they will want a slice of ours, if, like ourselves, they exceed the limit of necessity, and give themselves up to the unlimited accumulation of wealth.
GLAUCON: That, Socrates, will be inevitable.
SOCRATES: And so we shall go to war…without determining whether war does good or harm, thus much we may affirm, that now we have discovered war to be derived from causes which are also the causes of almost all the evil in States, private as well as public.
His premise here, stated more plainly, is that while the State arises from the needs of its members, those unjust aspects of the State arise from their unnecessary wants. It also stands to reason that as a State is successful in its fulfillments of those, more superfluous interests (whether by conquest, trade, or a potent mixture of the two) the more unsustainable that enlarged and entitled population will become. This is the story of Empire, played out time and time again in the human experiment but always with the same inevitable outcome of utter ruin for all.