What are the epithets in books 1-4 in the Odyssey?
Epithets are word or phrases of description that are repeated time and again within a work of literature. These words or phrases are a common feature of oral poetry because they help the teller remember the words and they help the reader identify the characters and their main characteristics. Thus in the Odyssey books 1 - 4 you will find several epithets including "bright eyed Athena" "sensible" Telemachus, "rosy fingered dawn" and "wise" Penelope. These examples are from the Penguin Classics translation: if you are reading a different translation, they may appear in a slightly different form.
Epithets are descriptive terms or glorified nicknames that are repeated often with someone's name. The difference between an adjective and an epithet is that epithets are only decorative. Adjectives do a lot for the context of the scene and the character, but epithets are linked to the noun by long-established usage, rather than immediate context.
One of the most common Homeric epithets is "rosy-fingered dawn" as a repetitive description of the time of day. Another common one is the "wine-dark sea." Most epithets have to do with specific characters, to emphasize their most prominent features as people. In the Odyssey, many common ones that show up include:
For Penelope: circumspect, wise, clever, cautious
For Athena: bright eyed, grey eyed, promachos (of war/fighting phalanxes), virgin, Pallas, hope of soldiers, whose shield is thunder, daughter of Zeus
For Odysseus: wise, clever, hotheaded, loved of Zeus/Athena, resourceful, much-enduring, much-pained, cunning, the great tactician
For Menelaus: red-haired/flame-haired, son of Atreus, war-like
For Nestor: sweet-spoken, charioteer
For Poseidon: earth-shaker
For Telemachus: poised, thoughtful
For Agamemnon: son of Atreus, wide-ruling, powerful
For Calypso: softly-braided, divinely-made, cunning, daughter of Atlas