Plato is the founder of political philosophy. The Republic is the first attempt to give a thorough and systematic account of how the common life of women and men ought to be structured. For Plato this means, above all, raising and answering the question of justice: what is justice and why should it be preferred to injustice? Answering this question would also mean describing injustice and showing why it is to be rejected.
The Republic is more than a work on politics in our narrower sense of the term. It is also more than a work on ethics, that is, on how the individual should live rightly and happily. It is also a work (in many cases the founding work in the Western tradition) on psychology, education, aesthetics, on what today we would call "sociology", and on philosophy in its more restricted meaning as epistemology (theory of knowledge) and ontology (which concerns itself with the nature of being). It is one of the relatively few books, philosophical or otherwise, that attempts a complete account of human life - of what it means to be a human being living well or living poorly. In it a complete philosophy of life is offered and defended. It is not merely the expression of an attitude. It is an attempt to demonstrate the one best or right way, or at least to show what must be proven and how it might be proven in order to reach this goal of knowing what is to be done.
Although often referred to as a "utopian" work, Plato is doing anything but building castles in the air. He is investigating as seriously as it has ever been done the question of justice - what does it mean in and for the individual, and in and for the city? But Plato's seriousness is not heavy-handed or pedantic. His writing is extremely elegant, and he is a master - again the first, and much imitated - of the dramatic form of the dialog. (Plato, after encountering Socrates, gave up a promising career as a poet in order to devote himself to what he felt to be the higher calling of philosophy).