Explain how this dramatic work of "Antigone" is actually a continuation of the plot that was startedin "Oedipus Rex."

Even though the play Antigone was actually written before the play Oedipus Rex, it tells the story of the daughter of Oedipus himself.  This is similar to George Lucas' Star Wars movies.  Lucas told the story of Luke before going back and producing the story of Luke's father, Anakin.  The basis of the father's story is given in the Luke stories, but later developed in their own movies, starting with The Phantom Menace.

Here, the story of Antigone is about a young woman, daughter of a king who has been deposed.  Oedipus, as king, discovered that he had killed his own father and married his mother.  He stabbed out his own eyes in self-punishment and wandered in exile until he died.  Creon has become the new king of Thebes.  He has a grudge against the children of Oedipus because Polyneices (Oedipus' son and Antigone's brother) had fought against him in the battle between Thebes and Argos.

This is where Antigone comes in.  Her brother Polyneices, dead at the hands of her other brother, has not been buried.  Creon won't allow it because Polyneices fought against him.  This means that Polyneices' spirit will never be at rest.  Antigone is fighting for the right she believes her brother - and her family - deserves.  Keep in mind, too, that Antigone and her siblings are related to Creon, as he is their uncle.

Besides dealing with the characters of Oedipus, the play deals with the conflicts as the original play as well.  Part of Creon's struggle with Antigone comes from his desperate desire to be as respected as Oedipus was.  Like Oedipus, Creon is figuratively "blinded" by his own pride, which leads him to act badly and to bring disaster upon his family and his kingdom.  He is left in the end like Oedipus - grief-stricken and distraught.