What is a fugue?

and for extra points!

why do musicians/composers study fugue?
which composers have studied fugue?

a contrapuntal composition in which a short melody or phrase (the subject) is introduced by one part and successively taken up by others and developed by interweaving the parts.

Explanation:

the above mentioned statements talks about the creativity of an artist and to what extend they can utilize and experiment on the objects provided.   differing size and subjects are given so that an image of wisdom is created. displaying a transition from light to dark in something by darkening sections in order to create a shadow. and lastly, putting bits and pieces together to formulate a new image.