From the characterization of Polyphemus, what conclusions can you draw about qualities that ancient Greek society considered barbaric or...

In the episode of the Cyclops, Homer comments on the differences between Greek civilization and the barbaric and monstrous Cyclopes who have no law.

Odysseus says to Alcinous:

"We sailed hence, always in much distress, till we came to the land of the lawless and inhuman Cyclopes. Now the Cyclopes neither plant nor plough, but trust in providence, and live on such wheat, barley, and grapes as grow wild without any kind of tillage, and their wild grapes yield them wine as the sun and the rain may grow them. They have no laws nor assemblies of the people, but live in caves on the tops of high mountains; each is lord and master in his family, and they take no account of their neighbours."

We see that essential to civilization are law and assembly.  The Greeks have both, and their gods have both.  But Polyphemus lives alone in his cave.

Important to keeping Greek society civil is the guest-host relationship. Greeks prided themselves on being good hosts: they were expected to take in any guest, and to feed, clothe, and give him shelter before he even asked his name.  In this way, Odysseus expects, as a guest, to be treated with civility.  He expects the owner of the cave to give he and his men cheese and lamb.  When Polyphemus refuses and eats Odysseus' men, Odysseus revenges according to the guest-host relationship.

He takes revenge on the giant by getting him drunk.  Odysseus turns the tables and plays host, giving the cyclops wine.  This sets the giant to sleep, giving Odysseus time to blind him.