Ancient Philosophy

In Book I of the Republic Socrates analyzes various definitions or accounts of Justice, beginning with Cephalus’ and ending with his own. What are the four definitions? What is wrong with them, in cases where there is something wrong? How does the notion of self-interest help to explain the progression of the arguments/definitions?

What are the parts of the soul and how does Plato argue for them? How does he account for, i.e. define, the virtues in terms of a tripartite soul? If you can, explain how the education of desires helps him account for the virtues?

Each topic has parts, so please address them all.