The vāhana or vahanam denotes the being, typically an animal or mythical entity, a particular Hindu deity is said to use as a vehicle. In this capacity, the vāhana is often called the deity's "mount".
The eight Matrikas riding different vahanas like (top row, second from left to right) Garuda, a peacock, Nandi bull, a hamsa (goose/swan); (bottom row, from left) buffalo, elephant and lion
A Bhagavata Purana manuscript page depicting the story of Atri and Anasuya meeting the Trimurti riding on their respective vahanas. (PhP 4.1.21-25). (Paper, late 18th century, Jaipur)
Ganesha, or Ganesh, also known as Ganapati, Vinayaka and Pillaiyar, is one of the best-known and most revered and worshipped deities in the Hindu pantheon and is the Supreme god in the Ganapatya sect.
Vahana
…are often emblematic of the deity it carries. Nandi the bull and vehicle of Shiva, represents strength and virility. Dinka the mouse and vehicle of Ganesha, represents speed and sharpness. Parvani the peacock and vehicle of Kartikeya, represents splendor and majesty. The hamsa, the vehicle of Saraswati…
Basohli miniature, c. 1730. National Museum, New Delhi
700-CE Kalinga-style Ganesha with shrew below, Someshwara Temple, Mukhalingam, Andhra Pradesh
A 13th-century statue of Ganesha, Hoysala-style, Karnataka
A typical four-armed form. Miniature of Nurpur school (circa 1810)