Here you will find a general overview of epic poetry as a genre. You will also find links to more specialized topics and to individual works.
"Epic," Princeton Encyclopedia of Poetry and Poetics.
Epic poetry begins with The Epic of Gilgamesh. It is unlikely that any Medieval or Renaissance European writer had read Gilgamesh.
The European epic traditon begins with Homer in Greece around 800 BC. It is essential that students of English literature read The Iliad and The Odyssey. The form of the epic poem, its typical characters, its plot, its tropes, and so forth are all set out in Homer. All epic poets of note read him. Other epic poets include Hesiod, Apollonius, Ovid, Lucan, and Statius.
The epic was written in dactylic hexameter in a dignified and elevated style. It typically begins with an invocation to a muse and contains elaborate desriptions, similes, and speeches. It tells of major events of historical importance (the fall of Troy, the foundation of Rome, the fall of man, etc.). Its characters are noble.
Virgil (70-19 BC) produces the great epic poem of the Roman Empire. The Æneid takes its name from a character in Homer's Iliad who leaves Troy and comes to Italy to found Rome. Every Medieval and Renaissance author of note read The Æneid and knew it well. It is a model for Milton's Paradise Lost.
Medieval epic poems are plentiful, though rarely read. Each nation or state produced its great epic poets. Italy has not only Virgil, but also Dante, among others. Dante's great epic is The Divine Comedy. It has inspired poets and artists for centuries. T. S. Eliot is said to have carried a volume of Dante in his coat pocket. Gustave Doré illustrated The Divine Comedy in the nineteenth century. Here is a gallery of Doré's drawings.
One of the great Spanish epics of the Middle Ages is El Cid, or more fully El cantar de mío Cid. Written or copied in 1207 by Per Abbat, it is the story of the conquest of Valencia by Rodrigo Díaz de Vivar, who lived during the time of the Norman Invasion (the end of the Old English period).
One of the great French epics of the Middle Ages is the Chanson de Roland. It tells the story of Charlemagne and an attack on his troops by Basques at Roncevaux in 778. The poem may have been written by Turold in 1090.
Two great German epics are The Heliand, a ninth-century version of the Gospels in Old Saxon; and The Nibelungenlied. The latter tells the story of Siegfried, Brunhild, Dietrich, Gunther, Hagen, and Attila the Hun. It was extraordinarily influential in German literature.
English epics begin with Beowulf. There are others in Anglo-Norman, which are largely unread today. A number of romances reach epic length, but not epic status. Piers Plowman is long, but not an epic. Chaucer writes an epic poem, Troilus & Criseyde, which was extremely well received in the fourteenth and fifteenth centuries.
During the Renaissance, Spenser's Faerie Queene is an epic. But perhaps first among euqals is Milton's Paradise Lost.