Lord Ganesha is an embodiment of wisdom and bliss. He is the Lord of Brahmacharins. He is the foremost among Brahmacharins or celibates.
He rides on the Vahana, the small mouse. He is the Presiding Deity of the Muladhara Chakra. He is the Lord who removes all obstacles in the spiritual path and brings worldly success. So He is called Vighna Vinayaka. His Bijakshara is Gang. He is the Lord of harmony and peace. Lord Ganesha represents OM or the Pranava. Pranava is the chief Mantra of the Hindus. Nothing can be done without uttering it. Hence the practice of invoking Lord Ganesha before beginning any rite or work. The two feet are His Jnana Sakti and Kriya Sakti. Lord Ganesha has the elephant-head as that is the one figure in nature which is of the form of Pranava. Riding on the mouse represents that He has killed egoism. He holds Ankusa. This represents that He is the Ruler of the world. This is the emblem of Divine Royalty.
Ganesha is the first God, Adi-Deva. Mouse is a small creature. Elephant is the biggest of all animals. Riding on a mouse and wearing the head of an elephant denote that He is the Creator of all creatures, from the biggest elephant to the smallest mouse. Elephants are very wise. Wearing the head of an elephant indicates that Lord Ganesha is an embodiment of wisdom. It also denotes the process of evolution. The mouse gradually evolves into an elephant and finally becomes a man. That is the reason why Ganesha has a human body, the head of an elephant, and mouse as His vehicle. This is the symbolic philosophy of His form.
He is the Lord of Ganas or groups, such as the group of elements, the group of senses, the group of Tattwas. He is the head of the followers of Siva.
The Vaishnavas also worship Lord Ganesha. They have given Him the name of Thumbikkai Alwar, i.e., Alwar with the proboscis.
Lord Ganesha’s two Saktis are Kundalini Sakti and Vallabha Sakti.