Shri Ganesh
The elephant-headed remover of obstacles, invoked at the start of any new venture, worship or journey.
Who Shri Ganesh is
Ganesha is the elephant-headed son of Shiva and Parvati, worshipped as the remover of obstacles (Vighnaharta) and the deity invoked first, before any undertaking — a new business, a wedding, an exam, even the writing of a scripture. The full story of how he came to have an elephant's head, involving Shani's cursed glance, is told in the Ganesh Chalisa.
Symbols and vehicle
He's shown with a large belly (said to hold the entire universe), a broken tusk (used, tradition says, as a pen to write the Mahabharata at sage Vyasa's dictation), and a fondness for modak sweets. His vehicle, curiously, is a small mouse (Mushak) — a deliberate contrast showing that even the largest being can be carried by the humblest, and that no obstacle is too small or too large for him to move.
His other names
Vinayaka, Ganpati, Gajanan (elephant-faced) and Lambodar (large-bellied) are among his many names, each capturing a different aspect of his form or role.
How he's worshipped
Ganesh Chaturthi, his major festival, is celebrated over several days with elaborate idol installations and worship before immersion (visarjan). The Ganesh Aarti ("Jai Ganesh Deva") opens most household pujas regardless of which deity the day's worship is centred on.