What are the main philosophical arguments of Plato's Gorgias?

Plato's Gorgias is divided into three main sections. In
the first, Socrates' interlocutor is Gorgias, in the second Polus, and in the third,
Callicles. The first section discusses the nature of rhetorical persuasion and whether
it can be taught as a purely technical art or whether the teacher of rhetoric must also
teach virtue. In the Polus section, the discussion of rhetoric extends to also include
the argument that in order to teach rhetoric well, the teacher must be one who knows the
virtues and thus a philosopher. Both the explicit arguments and the background of Polus
being Gorgias' pupil raise the question of whther the teacher is responsible for misuse
of teachings by pupils.

In the final section the
interlocutors discuss justice. Socrates makes the paradoxical claim that you should use
rhetoric to persuade judges to punish you when  you have done wrong. This is corollary
to the argument he raises that it is worsed to commit than to suffer injustice, because
the former harms the soul but the latter only affects one's external
circumstances.