Did the elizabethan era believe in greek mythology?What i noticed is that he refered to the greek mythology alot in his plays so was it part of his...

To the best of my knowledge most people in the Elizabethan
era (the late 1500's) did not actually believe in Greek
mythology. 

The vast majority of English people in the
Elizabethan era were either Protestant Christians (like the Queen) or Roman Catholics
(whom the Queen allowed to worship as they pleased).  Neither Protestant nor Catholic
theology ascribes to the belief in multiple, human-like gods such as those found in
Greek mythology. 

Nonetheless, the
stories of Greek mythology were well known to most Elizabethans,
particularly those who were well-educated.  To be considered well-educated, one needed
to have a thorough knowledge of the major characters in Greek mythology.  People looked
to these stories as important creations that contain great truths about human nature.  
That is why authors like Shakespeare make so many references to stories from Greek
mythology.