Story of Oedipus
Laius is the King of Thebes. He marries with Jocasta, and has a child. The oracles predict that this child, when grows up, will kill his father and marry his mother.Obviously, Laius does not agree and decides to kill his son. He secretly orders a soldier who does not kill the baby but leaves it in the forest. The child, with ankles broken and binded to a tree by a rope, is pitied by a herder couple, who picks it up and sends it to Polybus, the king of Corinth. He then was named Oedipus which in Greek, means "swollen feet". As a teen, he goes to Thebes city, not knowing who he is. He meets a old man (the king of Thebes, his father) who, because does not spare a pass to him, runs in struggle. Oedipus kills the old man. Upon entry in this city, he meets a woman Sphink defender of the city, a totally terrorisant: she is used to give riddles to the habitants who should not be saved without answering the given question. Until then, no one can pass her ridder. The Sphink give Oedipus such a riddle: "Which animal goes in 4 feet in the morning, 2 feet at noon and 3 feet in the evening?" Oedipus gives the reply ("human") and returns as hero to Thebes. The city proposes him to mount on the throne, since the place is open and free. He marries Jocasta, they have children and live in happiness for 15 years. Till one day the plague destroys the city which asks why to the oracle: "The plague is the punition from Gods to a parricide and an incest". Oedipus discovers it's relating to him. He pokes his eyes out of desperation, Jocasta hangs herself. Antigone follows him outside of the city which is chasing him. They leave to Athenes as their refuge.
The Oedipus Complex
"The psychanalyst make us understand more and more of the fundamental importance of Oedipus complex, and we can say that what separates adversaries and partisans of psychanalysis, is the importance that the lastest attaches to the fact" - Sigmund Freud -
(the original words were in German, but here is French, which I don't know quite well

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The word "complex" comes from latin and means originally "compound of diverse heterogenous elements". Applied by Breuer in the "Studies on Hysteria", it acquired, by assimilation to the German term "komplex", the sense of "what is complicated".
The story of Oedipus complex is related to the Freudian theory and also to the history of psychanalysis on the whole. On things concerning the development of a child, the pyschanalysis finds three basic stages: the Oral stage, the Anal Stage and the phallic stage. It's at the time of phallic stage that Oedipus complex occurs on the boy (Electra complex to the girl). The Oedipus complex is an organised (structural) whole of amorous desires and hostile desires that a child will experience in regard of their parents. In positive form, the complex presents as in the Oedipus story: want the same sex rival's death and opposite sex's sexual desire. In negative form, it shows the inverse: love parent of the same sex and hate or envy the parent of the opposite sex.
In fact the two forms meet in various degrees in the form said fully from Oedipus complex. Freud situate the Oedipus complex to a period of 3-5 years. It plays a basic role in the construction of the personality and in the orientation of human desire. Too early Freud poses the theoritic base of Oedipus complex as the besire for the parent of the other sex and hostility for the parent of the same sex. It is named first as "nuclear complex" and then "paternal complex". In 1910, in an article titled "Contribution to the psychology of the amorous life", the term "Oedipus complex" is used by Freud: "I have find in myself anyway, the sentiments of love against my mother and jealousy to my father, sentiments that I think, is common to all young children" (see archives "Freud").
Phallic Stage
Until then the father was deemed by the child as an auxiliary mother. The child goes to discover that the father has in fact a very particular function. It appears threatening, because unknown, representing a potential threat. The child goes closer to its mother. It goes to consider that the father interests the mother so much, and some times more than their demands to child. ® Attitude of anger and admiration for a person who owns mother. The child goes to put together the father's parental role with the mother's loving role. It's a division more difficult than asking himself who he is. The child gets lost in the first solitude of human. It replies to himself.
Recognition of Body
The child is focused on one point very important in its body: its genital organs. Displacement between the anal erotism and the urethral erotism. The child discovers that some persons have a penis and others don't have one. There are also ones who have them two or who don't have either. All the big persons should have a penis. It poses a lot of questions on the procreation, sexuality, growth, the relations between the parents.... Because of misunderstanding the responses, it will respond in its manner. It couldn't admit what doesn't correspond with its fundamental growth. The fertilisation is linked for him when he already knows the foogs ingestion, kiss.... For some aspects, it's enough to show off his genital organs in order for having a baby. The birth is anal, or by navel. They also elaborate on the fantasy of the "primitive scene". The child may have witnessed the sex of its parents, or only imagined what happens when he is not included (at the adult age they find what he feels when he listens to whisper between two yet-known persons, they imagine to be included and harassed).