Plato's Republic refers to an ancient book composed by the Greek philosopher Plato (424-348 B.C.E.). It is written as a dialogue between Socrates and some friends on the nature of human virtue. As with other works by Plato, it is a literary work that tries to present the thoughts and ideas of Socrates.
The topic of the Republic is human virtue, and how to construct a state or government which allows its citizens to be virtuous. It begins when one of Socrates' friends challenges him to prove that it is better to do the right thing, and be thought unjust, than to do the wrong thing, and be widely considered righteous.
The main virtue Socrates argues for is that of justice: for each person to do what he or she ought to do. If everyone in the state does his or her duty, then everyone will live harmoniously.
I won't go into the particulars of how Socrates proposes this, but along the way he discusses such topics as:
1. People should be given tasks based on merit and ability, not on birth or heritage.
2. The idea that the psyche has three parts, consisting of reason, the appetites, and that "spirited" portion which sides with one or the other.
3. That a well-run state promotes the virtues and advancement of people with ability. This state is the "republic" from which Plato gives the work its name, but the book is much more than political philosophy.
4. That we know something to be true only when we have a reason for knowing something; otherwise, it is just our opinion.
5. That the quest for knowledge goes along with the quest for morality, and is a worthwhile pursuit.
6. And finally he argues for a belief in the immortality of the soul, and reincarnation, so that everyone gets in life what he or she justly deserves. In effect, he presents a story to show that, in a larger context, life really is meaningful.
The Republic is thus a foundational document in western philosophy, and its tenets have governed many areas of western thought for centuries.