As your text explains, Plato is considered the father of political science. Within The Republic, he presents his theories on the foundations of a perfect government. Rather than a theoretical examination of government, The Republic is written in story form, as the main character Socrates explores the ideal way to form a city.
A largely studied portion of The Republic deals with Plato's cave allegory. The story goes something like this: You, as a person, find yourself within a cave, chained to the ground, facing a stone wall. You cannot stand, and all you know are the images that play out before you, which are the shadows cast by a light source from behind you. You cannot see behind you, but you know that there are others in the cave with you.
This is the only state you have ever known. It is your only reality of the world. Plato goes on to explain that then one day, people come and remove your chains, and take you out of the cave. As you can imagine, you are scared and frightful, and thus fight these individuals as they drag you into this new setting. However, over time you learn to accept the larger image of the world around you and come to understand life outside of the cave. You then attempt to go back into the cave to free others.
This story was Plato's attempt to explain the world around us. Just picture it: You are chained to the ground and all you can see in front of you is a cave wall. There is a light source behind you, which casts reflections on the wall.
What do you think you would think of these reflections? Could they represent family members? Or friends? What about a god?