There are hundreds of stories concerning the intrigues and affairs of Greek gods and heroes. For a speech topic, you could focus on the legends of a specific Greek figure, highlight a part of the mystical world of Greek mythology itself or describe how the myths have influenced the cultures of the world.
Realms of Greek Mythology
The ancient Greeks divided their world into three realms -- the mortal plane, the underworld of Hades and Mount Olympus, where the gods resided. If your audience is unfamiliar with the Greek cosmos, describing the gods, their powers and their domains is a great way to quickly bring them into the world of Greek mythology. If you want to educate your listeners on a more specific topic, pick a specific god, his domain and one or two of the myths surrounding him. For example, if you are focusing on Hades, you might describe how he is the god of the dead and lord of the Underworld, and go on to describe the different regions of the Underworld --Tartarus, Asphodel, and Elysium -- and the different types of dead souls inhabiting each. You could also include the myth of how Hades came to rule the underworld by casting lots with his brothers, and his abduction of Persephone in order to be his bride.
Greek Creation Myth
While Greek gods, heroes and monsters are relatively well known, the Greek creation story is a topic less frequently explored. A lesson in how the Greek cosmos came to be is an opportunity for your audience to learn about a topic they might not already be familiar with. You can either compare and contrast the creation myth to those of other cultures and religions, or focus on a specific section of the myth that intrigues you, such as the triumph of the Olympians over the Titans or the birth of Uranus and Gaea. There are also many figures in Greek myth -- such as the goddesses Nyx and Eris, the furies and the nymphs -- who were born before either the Titans or the Olympian Gods. Focusing on these lesser-known characters is a great way to explore a new and exciting area of the Greek tradition.
Drama and Poetry
Ancient Greek culture comes down to us not only through recorded myths but also through the poems of Homer and the dramas of the ancient Athenian playwrights. Picking one play, such as Aristophanes' The Clouds or focusing on a specific topic, such as the portrayal of Athena in Greek literature, is a good way of providing your speech with focus and direction. If you are, for instance, speaking on the subject of hubris, or pride, as a fatal flaw in Greek heroes, you might cover how these protagonists suffer as a result of their pride. Ajax, for example, ultimately commits suicide as a result of refusing Athena's aid, and Odysseus is subjected to an excruciatingly long journey home for believing he is clever enough to outsmart Poseidon, god of the sea. Be sure to include quotes from these works where appropriate. Greek dramas often include a chorus which serves to explain the action and themes of the play to the audience.
Mythology and Modern Culture
The language and characters of Greek mythology are still alive and well today, from Freud's Oedipus complex to the video game God of War to the sneaker-company Nike, which takes its name from the Greek goddess of victory. Showing how Greek mythology continues to inform and enrich our culture can be an excellent way to capture your audience's interest. For example, a topic focusing on how Greek gods and heroes continue to influence our notion of heroism might highlight how superheroes Wonder Woman and the Flash take their design from the Amazons and Hermes, and the ways Disney's Hercules reinterpreted the legend of Heracles. Be sure to highlight both how modern imitations resemble and change the myths they are based on; for example, Hercules casts the goddess Hera as Hercules' mother, while in myth his mother was the mortal Alcmene.
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