Short answers, pulled from the story.
The Epic Cycle was a collection of eight ancient Greek epic poems composed in dactylic hexameter, all related to the story of the Trojan War. Two of the eight, the Iliad and the Odyssey, survive complete; the other six are known only from fragments and later summaries.
The Epic Cycle includes the Cypria, the Iliad, the Aethiopis, the Little Iliad, the Iliupersis, the Nostoi, the Odyssey, and the Telegony. The term most often refers specifically to the six non-Homeric poems, distinguishing them from Homer's Iliad and Odyssey.
The six non-Homeric poems of the Epic Cycle survive only in fragments and summaries from Late Antiquity and the Byzantine period. The most detailed account of their plots comes from a damaged preface in a 10th-century manuscript of the Iliad known as Venetus A, which is itself derived from a lost work called the Chrestomathy by a figure known only as Proclus.
The most common ancient attributions give the Cypria to Stasinus, the Aethiopis and Iliupersis to Arctinus, the Little Iliad to Lesches, the Nostoi to Agias or Eumelus, and the Telegony to Eugammon. The Iliad and Odyssey are attributed to Homer.
Neoanalysis is the modern scholarly term for the study of the relationship between Homer's epics and the rest of the Epic Cycle. Some Neoanalysts argue the Homeric poems drew directly on the Cyclic poems; others hold that all the epics shared a common legendary tradition that predated both.
In the Telegony, a two-book poem attributed to Eugammon, Odysseus travels to a region called Thesprotia before returning to Ithaca. He dies there at the hands of Telegonus, his illegitimate son.