There are two main Homeric poems, the Iliad (meaning the story of Troy) and the Odyssey (meaning the story of Odysseus).
Arguments about whether the Homeric poems originated as the work of a single poet and when they were composed and written down will go on for ever, though most experts now accept that they existed in some sort of oral tradition before they were standardised in writing. In standard, written form, they probably predate Virgil by at least five or six hundred years: in outline and inspiration, they go back in an oral tradition Heaven knows how much further. In spite of their age, the poems remain genuinely exciting: reading them, you feel the breath of the bronze age on your cheek. Their metre – Hexameters – is a defining feature, giving them a vivid rhythmicality and a powerful narrative flow which are impossible to convey in translation. To give an impression, there is a sound file and close translation of the opening lines of the Iliad and the Odyssey on Homer’s page in the poets section.