What is the notion of justice for Plato?
Plato discusses justice at great length in several dialogues including Apology, Laws, Republic, and Gorgias. His views of justice are generally concerned with what is called eudaimonia, or "living well". In other words, a just society in one which creates the preconditions for the philosophical life. The just society should be a mirror of the balanced philosophical soul which itself is an imitation of the form of the good.
Social systems of justice, legal systems, and systems of punishment are focused on improving the individual who violates them. To commit and injustice is worse than to suffer one as the committer injures his own soul but the suffer only is injured with respect to material conditions (which are inherently trivial). Punishment is intended to increase awareness of the committer of unjust deeds of his/her errors and thus serve to help them improve rather than as retribution or restoration.