Connections Between   Greek Mythology and Psychology   
Greek mythology consists of folk tales that were passed down by word of mouth in ancient Greece and were eventually recorded Some were based on factual events and some were formulated for entertainment or religious purposes.  Psychoanalysis is based on the idea that most of what makes us human is deeply hidden within our unconsciousness.  Some ways we can truly know our inner thoughts and desires are through dreams and unintentional actions and conversation.  An example would be stories that we think come from our imagination when in fact they probably symbolize an inner desire or fear.  A psychoanalyst would argue that Greek mythology is a supreme example of "ethnic imagination".  These stories had to start form somewhere and were probably added to and exagerated upon.  The result is a collection of myths that symbolize the unconscious drives of an entire civilization.  Some myths are used today in psychology to help explain abnormal behavior.
Examples of Greek mythology that have strong connections to psychology
Narcissus and Narcissism
The Oedipal Complex
The Electra Complex
Bacchus and Mass Hysteria

                                 
References
Dowden, Ken. 
The Uses of Greek Mythology.  London, 1992.
Grimal, Pierre. 
The Dictionary of Classical Mythology.   Paris, 1951.
Holmes, David S. 
Abnormal Psychology, Third Ed.  New York, 1997.
Pinsent, John. 
Library of the World's Myths and Legends.  New York, 1969
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