Our story begins as Socrates and his friend Glaucon head home from a festival. Ready to call it a night, they're intercepted by a whole gang of their acquaintances, who eventually convince them to come hang out at Polemarchus's house and have a nice, long chat.
Once they all arrive at the house, Socrates sees Polemarchus's father, Cephalus, who's an old friend. The two begin a conversation about the pros and cons of being old. As they continue to chat, their topic gradually shifts from old age to the idea of justice, and that's something that gets everyone's attention.
Cephalus bows out at this point, and his son Polemarchus starts debating with Socrates about the nature of justice. They start talking about: 1) what justice really means, and 2) whether justice is actually a good and useful thing to have in the real world. Word.
As Polemarchus becomes more and more convinced by Socrates, another guest, Thrasymachus (who seems to have a bit of anger-management problem), interrupts. He's kind of a bully, and he attacks Socrates for his style of arguing. Socrates is kind of freaked out, but he agrees to continue debating the issue of justice with Thrasymachus, who thinks that it's all about strength, not goodness.
After Socrates and Thrasymachus debate for a while, Glaucon jumps in and wants to hear more about the idea of the good. He also tells a little story about a ring of invisibility to help him make his point about justice—until Adeimantus, another guest, intervenes and argues further with Socrates about justice. This whole arguing thing should be sounding mighty familiar.
Finally, Socrates comes up with the idea that the best way to tackle the problem of justice is to invent an imaginary city, and so, voilà, that's what they do.
The guys describe a whole range of elements in this city—industry, employment, wealth, health, etc.—spending a lot of time on education and famously deciding that most poetry and music will be censored by the city's rulers (called guardians) because it often celebrates negative things. Bummer.
Finally, the guys get back to the topic of justice. By comparing the organization of their city to the organization of the human soul, they come up with this famous three-part division of the soul: 1) the rational part, 2) the spirited part, and 3) the desiring part.
Socrates then tries to continue discussing justice, but Glaucon interrupts and asks Socrates to say more about the status of women and children in the republic—he's just so curious. Socrates agrees and shows how women will have essentially equal rights as men.
Once they've established the domestic side of things, Socrates describes how the guardians of their city will also be philosophers, and from there, he begins an extended discussion of what philosophy is.
As part of their conversation describing philosophy, Socrates defines "the good" and his theory of "the forms." To help everyone understand these concepts more easily, he tells them a famous story often referred to as the Allegory of the Cave.
After finishing up the conversation on philosophy and education, Socrates then goes on to discuss the issue of government. He outlines five kinds of governments that exist and suggests that each one is developed out of another in a cycle: 1) Aristocracy, 2) Timocracy (a government all about honor), 3) Oligarchy, 4) Democracy, and 5) Tyranny.
In order to understand fully which of these governments is best, the guys briefly get into a conversation about desire, which ultimately leads them back to the hot topic of poetry. Socrates again condemns poetry, this time because it's a distortion of reality.
The whole conversation ends with Socrates telling a story called the Myth of Er, which is about a trip to the underworld. It's an abrupt— but final—end.