Story of Ekadanta Avatar:
As the name “Ekadanta” suggests, in this avatar or incarnation, Lord Ganesha was seen with only one tusk. In this avatar, Lord Ganesha had four arms, one tooth, a pot belly, and His head was very similar to that of an elephant. In this incarnation, His mode of conveyance was a mouse. Lord Ganesha was reincarnated to defeat demon Madasura.
As per the Padma Purana, once sage Parashurama had come to Lord Shiva’s place and was seeking a “Darshan” of Lord Shiva. But Lord Ganesha didn’t allow him inside as it would have Lord Shiva was sleeping at that time and Ganesha didn’t want His father’s sleep to be disturbed. Sage Parashurama was losing his patience and began insisting that he should be permitted to go inside and meet Lord Shiva but Lord Ganesha was adamant and finally, a fight between the two broke out. In the process of fighting each other, sage Parashurama threw his axe at Lord Ganesha. The moment Ganesha saw the awe, He could realize that this very awe was given to Parashurama by His father, Lord Shiva. After recognizing the axe, He refused to intercept the axe. He bowed down out of respect towards His father and took its full impact on one of His tooth or tusk which immediately broke. This broken tusk was used by Lord Ganesha to write the epic, Mahabharata. Lord Ganesha, who is also known as the embodiment of wisdom, was the one whom sage Vyasa dictated the Mahabharata. Therefore, He is accepted as the God of learning and patron of letters.
In this avatar, Lord Ganesha defeated the Madasur who was known as the embodiment of arrogance.