Plato's Republic is no easy read. Do not despair. You are not alone in wondering what it all means. It will take many readings, most of which will happen over the course of your life, to grasp most of the themes and meanings contained in the book.
The Republic should not be read as if it is a book offering solutions to political problems. It is, rather, like a piece of literature. It is perhaps useful to view it as a play, a great drama play that is.
That said, turn to this useful site to help you put together the framework for what we will discuss in class. See The Classic Pages: Plato.
Wikipedia.org also has a useful general discussion of The Republic to help you get started.
As you make your way through your readings here please make sure that you pay attention to how Plato (via Socrates) defines justice, a just/ideal Polis, and his creation of three categories in the ideal state.
Also, think through his critique of the 4 bad kinds of regimes. They are: Timarchy; Oligarchy; Democracy; and Tyranny.
Which kind of government does Plato say is best?
Good luck.
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