Ganesh explained - This God of knowledge and the remover of obstacles is also the older son of Lord Shiva. Lord Ganesha is also called Vinayak ( knowledgeable ) or Vighneshwer (god to remove obstacles). He is worshipped, or at least remembered, in the beginning of any auspicious performance for blessings and auspiciousness.
He has four hands, elephant's head and a big belly. His vehicle is a tiny mouse. In his hands he carries a rope (to carry devotees to the truth), an axe (to cut devotees' attachments), and a sweet dessert ball -laddoo- (to reward devotees for spiritual activity). His fourth hand's palm is always extended to bless people.
A unique combination of his elephant-like head and a quick moving tiny mouse vehicle represents tremendous wisdom, intellegence, and presence of mind.