Ganapathy
Ganapathy is elephant headed god and is the son of Shiva. Ganapathy attained universality when he defeated his brother Karthikeya in a competition sponsored by their parents. Both Ganapathy and Karthikeya were ordered by their parents to go around the universe. Karthikeya embarked upon the task and began the journey while Ganapathy simply walked around Shiva and Parvathi in few seconds. He took the right step as Shiva and Parvathi are the source of all existence in the universe and therefore they are the universe according to the Hindu mythology.
There are different versions about Ganapathi having an elephant head. One version is that Parvathi created Ganapathi in the absence of Shiva for the purpose of guarding her quarters. Shiva wanted to see Parvathi. Not knowing Shiva is his father and the husband of Parvathi Ganapathy disallowed him. The angered Shiva cut his head. Later, realizing the mistake Shiva restored life to Ganapathy with an elephant head. Another version is that Ganapathy’s head was burned when Saturn was forced by Parvathi in order to look at her child and bless him.
Ganapathy’s vehicle is rat. It represents subjugated demon of vanity and impertinence. Look at the image of Ganapathy. The Conch in hand represents sound which creates sky. The Laddu (a small ball-like sweet) represents truth. The Snake represents control over poison (of the passions). The Hatchet represents the cutting away of the bondage of desires. The Mudra represents fearlessness. The broken Tusk is the tool with which he wrote the Mahabharatha.
All Tantric and Spiritual worships in Hindu tradition are began with a Ganapathy Homam (homage). Prior to house-warming or beginning a business a Ganapathy Homam is conducted. In almost all temples prior to the festivals Ganapathy Homam is conducted. In short, a Ganapathy Homam precedes initiation of any venture or good thing in Hindu tradition.