According to Plato, what was the central question of The Republic?

In The Republic, Plato is outlining the ideal society. He grapples with many difficulties in the ideas of how to make the society truthful, just, and upright, and my personal favorite is the belief that poets should be excluded. However, that is not the main point of this text.
Justice, Plato reasons, is the centerpiece of the ideal society, so the main question throughout this book is this: what is justice, and how do we act justly in our lives? Plato presents the argument that justice is in our best interests in every situation, something that is not always self-evident. This is a contradiction of the idea of doing whatever it takes to get ahead, without regard for others. If everyone acts justly, the perfect society will practically build itself, and it will be utopian in nature, Plato reasons. An understanding of what justice is, which is a major theme in this work, is fundamental to acting justly in everything we do.