Interestingly, the mighty Ganesha rides the meak rat. This again has a philosophical meaning. The elephant God can crush all hurdles and the rat can drill its way through the narrowest of crevices.
Thus Ganesha embodies knowledge, learning, spirituality, power, humility in the nutshell-the Brahman.

There are many tales about how Ganesha got His elephant head and also a place of previeledge among all gods. Shiva Purana states that Goddess Parvati once wanted to have a bath, She wanted to have someone to stand guard at the entrance. So She created a boy out of the dirt of her body and infused life into it. She asked him to let no one in. Meanwhile, Lord Shiva came there and wanted to meet Parvati. Ganesha prevented him from going inside citing his mother's command. Lord Shiva got enraged and cut off the boy's head. When Parvati came out she was unconsolable with grief. To pacify her Shiva asked His troops to get the head of any creature sleeping with his head pointed in the North. They brought back the head of an elephant as that was the only creature they found sleeping with his head in the North. Shiva joined the head of the elephant with that of the boy's trunk and brought him to life. Parvati was still not satisfied with the elephantine head. Shiva blessed him that He would be the foremost of all Gods and His blessings would be sought by everyone before the onset of every enterprise. To this day and age no work of devout Hindus is begun without invoking Him. He is symbolised by the Swastika.

Another myth holds that Mata Parvati begot a charming young infant boy. All Gods arrived to have a look at the baby and bless him but Shani, the son of Surya (the Sun God) kept his eyes rooted to the ground. Parvati felt hurt she asked Shani the reason for his behavior. To this he replied that casting his glance over the baby would harm him. Parvati insisted that he should look at the young one. Shani obeyed and due to his malefic glance, the baby's head got severed. Everyone present was aghast and grief struck. Thereupon the head of an elephant was brought and transplanted.