I mistakenly called this the theatre earlier, however, this is the Odeon near the State Agora.

From the Wikipedia: "Odeon (from the Ancient Greek ᾨδεῖον, Ōideion, literally "singing place", or "building for musical competitions"; from the verb ἀείδω, aeidō, "I sing", which is also the root of ᾠδή, ōdē, "ode", and of ἀοιδός, aoidos, "singer") is the name for several ancient Greek and Roman buildings built for music: singing exercises, musical shows, poetry competitions, and the like."

I took this picture from slightly outside, to the left you see the space of the State Agora.