Sophocles is considered one of the great ancient Greek tragedians. Among Sophocles' most famous plays are
Oedipus the King,
Oedipus at Colonus, and
Antigone. These plays follow the fall of the great king, Oedipus, and later the tragedies that his children suffer. The
Oedipus plays have had a wide-reaching influence and are particularly notable for inspiring
Sigmund Freud’s theory of the "Oedipus Complex," which describes a stage of psychological development in which a child sees their father as an adversarial competitor for his or her mother’s attention (or in non-psychology speak, it’s the kill-the-father-sleep-with-the-mother complex).
The three plays are often called a trilogy, but this is technically incorrect. They weren't written to be performed together. In fact they weren't even written in order.
Antigone, which comes last chronologically, was the play Sophocles wrote first, around 440 B.C. It wasn't until about 430 B.C that Sophocles produced his masterpiece
Oedipus the King. He finally wrote
Oedipus at Colonus in 401 B.C., near the end of his life. Also note that the plays were rarely if ever revived during the playwright's life time, so it's not like it would have been easy for Sophocles' audiences to compare them.
These facts probably explain some of discrepancies found in the plays. For example, while Creon is the undisputed King at the end of
Oedipus the King, in
Oedipus at Colonus it’s Polyneices and Eteocles who are battling for the throne. In
Antigone, Creon assumes the throne with no mention of the fact that he's ever sat on it before. It's pretty unlikely that Sophocles forgot this key fact. But it could very well be that it just didn't matter very much. Each play is a separate interpretation of the myth, not a part of a trilogy. Sophocles would've been under no obligation to make the plays coherent in every detail.
Of course, while the plays aren't technically a trilogy and do have discrepancies, they do share many similarities. Several of the key characters put in repeat appearances, including Oedipus, Creon, Teiresias, Ismene, and Antigone. Also, the plays have a lot of the same themes. The plays all deal in some way with the will of man vs. the will of the gods. Self-injury and suicide also plague the family until the end. It seems that Oedipus's family is never quite capable of escaping the pollution of his terrible mistakes.