Gam Gam Ganapati Sharanam Ganesha
गं गं गणपति शरणं गणेश
gaṃ gaṃ gaṇapati sharaṇam gaṇesha
gaṃ: Bija mantra (condensed sound form) for Ganesha.
gaṇapati: Another name for Ganesha with similar meaning, as the lord ("pati") of Shiva's army ("gaṇa").
sharaṇam: To take refuge. In this case, to take refuge in Ganesha.
gaṇesha: The elephant-headed god, son of Shiva and Parvati, who is the lord/leader ("Isha") of Shiva's army ("gaṇa"). Shiva's army is made up of all sorts of strange creatures, huligans of heaven ("gaṇa"), as he will use any means, devious or not, to remove ignorance in the devotee.
"Ganesha is the formless Divinity, encapsulated in a magnificent form for the benefit of the devotee." ~ The Art of Living
"Ganesha, also known as Ganapati and Vinayaka, is one of the best-known and most worshiped deities in Hinduism. His image is found throughout India. Hindu sects worship him regardless of affiliations. Devotion to Ganesha is widely diffused and extends to Jains, Buddhists, and beyond India. There is also a sect of devotees called the Ganapatya, who identify Ganesha as the supreme deity. The principal scriptures dedicated to Ganesha are the Ganesha Purana, the Mudgala Purana, and the Ganapati Atharvashirsa." ~ wikipedia
"Seed syllables (bija mantras) are fundamental sound vibrations that make up the energy of the universe. They are the quitessence of a mantra, the sonic condensation of a deity. Ganesha's bija is 'Gam,' also sometimes spelled Gang, Gung or Gum." ~ anonymous