Short answers, pulled from the story.
The Theban Cycle is a collection of four lost ancient Greek epics that told the mythological history of the Boeotian city of Thebes. The four poems are the Oedipodea, the Thebaid, the Epigoni, and the Alcmeonis, all composed in dactylic hexameter verse and believed to have been recorded between 750 and 500 BC.
Authorship varies across the four poems and is often uncertain. The Oedipodea has been attributed to Cinaethon of Sparta. The ancient elegiac poet Callinus believed Homer authored the Thebaid, a view widely recognized in antiquity, though the true author cannot be determined. The Epigoni has been attributed both to Homer and to Antimachus of Teos. The Alcmeonis has no known author, and its date of composition is also unknown.
In the Oedipodea, the Sphinx is described as a force that "devours great and small," rather than a gate-guardian that kills only those who cannot answer its riddle as in Sophocles. The Oedipodea also states that Oedipus's children came from a separate marriage, not from his unknowing union with his mother Epicaste, as Sophocles depicts.
The Epigoni presumably told the story of a second expedition against Thebes, led by the sons of the seven commanders who had failed in the first campaign, set ten years after that original attack. Fewer than ten fragments survive in total, with only three verbatim fragments amounting to four lines, including the poem's first line: "But now, Muses, let us begin on the younger men."
The Alcmeonis tells the story of Alcmaeon killing his mother Eriphyle because she arranged the death of his father Amphiaraus. Only seven records of the poem survive in all of ancient literature, and its length, author, and date of composition are all unknown, making it the least understood epic in the Theban Cycle.
The Theban Cycle influenced ancient Greek drama, including works by Sophocles, Euripides, and Aeschylus, some of which are still performed today. The Thebaid was also likely the basis for a later Latin epic of the same name that was popular through the Middle Ages and the Renaissance. In 2002, the Düsseldorf Schauspielhaus staged a production called Theban Cycle combining four interconnected Greek plays by those three dramatists.