Short answers, pulled from the story.
An odeon (or odeum) is a type of ancient Greek and Roman building designed for musical activities including singing, musical shows, and poetry competitions. Odeons were typically smaller than open-air theatres and were built with a roof to improve acoustics.
The word odeon comes from the ancient Greek ᾠδεῖον, which derives from the verb aeidō meaning "I sing." The same root produced the Greek words ōidē (ode) and aoidos (singer).
The oldest known odeon in Greece was the Skias at Sparta, said to have been built by Theodorus of Samos around 600 BC. Its name came from its resemblance to the top of an umbrella.
Pericles built the Odeon of Athens in 435 BC at the southeastern foot of the Acropolis. The mainly wooden building was described by Plutarch as "many-seated and many-columned" and was said to be decorated with the masts and spars of ships captured from the Persians.
The Odeon of Herodes Atticus was built around 160 AD by the wealthy sophist and rhetorician Herodes Atticus in memory of his wife. It could accommodate between 4,500 and 5,500 persons and featured a ceiling of beautifully carved cedar wood beams.
The first odeon in Rome was built by the emperor Domitian, and a second was built by Trajan. The form also spread to provincial cities, with examples recorded at Catania and Taormina in Sicily, Plovdiv in Bulgaria, and Lyon in Gaul.