What did plato critique in his book the republic?

Before Plato wrote The Republic, there were two political parties vying for power in Athens: the oligarchs (give power to a few) and the democrats (give power to all). Plato realizes the faults of both sides, whose members cause bloodshed, causing him to offer a new politics: a republic (hence the title of the book). In this book, Plato specifically critiques democracy as a system that provides no order over the people, thus resulting in their ability to do whatever they want, despite the (often bloody) consequences.