In the woods, a farmer watched Indra worshipping a Linga under a tree. He reported this to King Kulasekara, who cleared the forest, built a temple for the linga and a city around the temple. When it came to the naming, Shiva appeared, a drop of nectar (madhu) fell from his hair onto the city and it was called Madurai.
In Madurai Shiva and Parvati dwell as Sundareshvara and Minakshi. Paranjothi Munivar depicts in his Tiruvilaiyadal Shiva’s divine play (vilaiyattu) in Madurai.
For the story of Minakshi visit
http://utkarshspeak.blogspot.com/2012/12/queen-of-madurai.html?m=0