For it is impossible or not easy for someone without equipment to do what is noble: many things are done through instruments, as it were—through friends, wealth, and political power. Those who are bereft of some of these...disfigure their blessedness, for a person who is altogether ugly in appearance, or of poor birth, or solitary and childless cannot really be characterized as happy... (1.8.1099b31-1099b5)
Aristotle shows what we might consider a "modern sensibility" when it comes to his understanding of what it takes to do the right thing. He's speaking here of the advantages of privilege (i.e. having the "equipment to do what is noble") and the great disadvantages that come when a person is without. Without certain goods, a person has a much harder time being virtuous, and as a result, difficulty being completely happy. His narrow concept of what it means to be happy is both thoughtful (considering disadvantage) and a bit elitist (writing off those without privilege).
Now, things that come about as a result of force or on account of ignorance seem to be involuntary. That which is forced is something whose origin is external, since it is the sort of thing to which the person who is acting or undergoing something contributes nothing...(3.1.1110a-3)
Aristotle wants to discuss voluntary and involuntary behavior in order to determine what is just in judging the actions of others. It's helpful for lawgivers especially to understand what motivates behavior in assessing who/what is blame- or praiseworthy. The crucial point here is that involuntary behavior does not have its origin in the person acting. When personal agency is taken away from a person, he doesn't get to choose. Whatever happens, for better or worse, doesn't belong to that person.
[The tactful or witty person] will not do just anything or everything, of course, since a joke is a kind of slander and legislators prohibit the slandering of some things, but they perhaps ought also to prohibit joking about some things. The refined and liberal person, then, is disposed in this way, he being like a law unto himself. (4.8.1128a29-31)
Two different views of "judgment" are active in this passage. First, there's the correct reason of the witty or tactful person that allows him to judge how properly to joke and please his friends. Then, there's the more legalistic meaning, in which a person might be subject to the law if he lacks tact and moral judgment. It makes perfect sense, then, that the person who uses correct reason can be judge of the situation (i.e. "a law unto himself"), since he knows how to walk the line between amusement and slander.
The just, therefore, is what is lawful and what is equal; the unjust is what is unlawful and what is unequal. (5.1.1129b1)
Aristotle defines the just and the unjust in two ways here. First, according to the law: the just embrace legal code, whereas the unjust are lawbreakers. Then, he brings in the societal component: the unjust always grasp for more than their share of the pie (and are therefore "unequal"). This understanding of what's just and unjust will be important later, when Aristotle talks about the different kinds of justice (i.e. corrective and distributive).
The laws pronounce on all things, in their aiming at the common advantage, either for all persons or for the best or for those who have authority, either in accord with virtue or in some other such way. As a result, we say that those things apt to produce and preserve happiness and its parts for the political community are in a manner just. (5.1.1129b15-19)
Aristotle sees the law as the main preserver of equity and peace in society. It's the job of lawgivers to look into all aspects of human behavior and life in order to make the kinds of laws that will produce good citizens (by setting clear and reasonable boundaries) and promote justice (correcting inequalities, punishing lawbreakers).
Worst, then, is he who treats both himself and his friends in a corrupt way, but best is he who makes use of virtue not in relation to himself but in relation to another. For this is a difficult task. This justice, then, is not a part of virtue but the whole of virtue, and the injustice opposed to it is not a part of vice but the whole of vice. (5.1.1130a6-11)
Aristotle makes sure we understand how incredibly different it is to be just. We have to set aside self-interest and consider others as we would consider ourselves. Because it's so extraordinarily hard, justice requires extraordinary powers of goodness. But the effort's worth it, because the alternative is frankly quite terrifying. Giving in to unjust behavior makes us into one nasty piece of work.
One form of partial justice...is found in the distributions of honor or money or any of the other things divisible among those who share in the regime (for in these things it is possible for one person to have a share that is either unequal or equal to another's). The other form of such justice is the corrective one involved in transactions...(5.2.1130b30-1131a1)
This "partial" type of justice is different from justice as a whole—which Aristotle defines as the whole of virtue in relation to others—and deals specifically with equality. Distributive justice ensures that everyone in a community has access to goods held in common. Corrective justice applies to interactions between people, whether they're voluntary (where both parties agree to interact) or involuntary (where one party doesn't agree, as in assault). In both cases, the law intervenes to maintain balance in society.
Hence when people dispute with one another, they find refuge before a judge. To go to a judge is to go to the just, for a judge wishes to be, as it were, the just ensouled. And people seek a judge as the middle way, and some call them mediators, on the grounds that, if they hit the middle term, they will have hit on the just. (5.4.1132a20-24)
In his thinking about justice, Aristotle shows how corrective justice aims to re-distribute the harm done in a dispute so that each party has a more equal share of it. The judge's job, then, is to inflict loss on the person who tries to gain more than his fair share of something from someone.
We're not speaking only in terms of money here; "gain" might mean injuring someone and gratifying our passions by doing so. While the judge can't take away the injury, he can strike down the unjust person in some way, so that the hurt's equal on both sides. But it takes a right-thinking person to be able to find that balance, so the judge really does have to be a model of correct reason and just behavior.
The just exists for those for whom there is also law pertaining to them, and law exists among those for whom there is injustice. For justice is a judgment about the just and the unjust. (5.6.1134a30-33)
You've probably never gotten this basic in your thinking about justice, but Aristotle challenges us to think about that molecular political unit that makes both law and justice a Thing: the community. If we don't live together (i.e. share a life in common), there would be no need to regulate anything. Without laws, there are no lawbreakers. While we might disagree (people can still hurt others, even in the absence of laws), Aristotle's correct in an absolute sense: justice and injustice in a specific sense can only exist when we group up and agree on the terms of living together.
The just peculiar to a slave master and to a father are not the same as these [political senses] of justice, though they are similar. For there is no injustice in an unqualified sense toward one's own things, but one's property or offspring...is like a part of oneself, and nobody chooses to harm himself. (5.6.1134b9-12)
Aristotle's declaration regarding both slaves and offspring (and one can add wife to this list) highlights the very narrow application of the concept of justice in this work. While justice as a general concept doesn't encompass these relationships, Aristotle believes that there's a more natural sense of justice that should regulate virtuous behavior toward these marginalized human beings.
Of course, without the application of general or particular justice in these cases, it means that the law won't legislate concerning them—which means that there's no sense that these people can ever be wronged (and so: no justice if they are).
This is in fact the nature of the equitable: a correction of law in the respect in which it is deficient because of its being general. For this is the cause also fo the fact that all things are not in accord with law: it is impossible to set down a law in some matters, so that one must have recourse to a specific decree instead. (5.10.1137b27-29)
Aristotle understands that the law isn't perfect in its interpretation of what's just or unjust and lays the blame for that at the feet of non-specificity. Because lawgivers can't always legislate for every specific case that might come before them, there's bound to be a moment when the law fails to do what is right.
This is where the concept of equity comes in. Note that "equity" is not the same as "equality": while equality ensures that people have the proper proportion of the good, equity is the principle that perfects justice. It's the back door that allows an equitable person to make corrections to the law to restore the balance of society in specific cases.