Ganesha is considered to be the Lord of letters and learning. In Sanskrit, the word Buddhi is variously translated as knowledge, wisdom, or intellect. The concept of buddhi is closely associated with the nature of Ganesha, especially in the Puranic period, when many myths stress his cleverness and love of intelligence. One of Ganesha's names in the Ganesha Purana and the Ganesha Sahasranama is Buddhipriya or "Fond of Intelligence''. The word Priya can mean "fond of". This name also appears in a list of 21 names at the end of the Ganesha Sahasranama that Ganesha says are especially important. Lord Ganesha’s parents are Lord Shiva and Parvati. His siblings are Kartikeya, his brother, and Ashokasundari, his sister. His pet is a mouse and is called Mooshakraj.
Ganesha was first the son of Parvati when she first went away from her husband, Lord Shiva. She stayed in a cave and paranoid Lord Shiva went to search for her. He sent a bunch of his men to search for Parvati. Eventually, when they found the cave that Ganesh and Parvati were living in, Parvati went out and Ganesh was instructed to protect the house, which he did. He fought all the men until eventually, Lord Shiva had no choice but to handle Ganesha himself. When he reached the cave, Ganesha said the same thing that he is protecting the cave as his mother, Parvati had instructed him to do so. Lord Shiva and Ganesha fought until Lord Shiva, decapitated Ganesha’s head. When Parvati arrived in the cave, she saw Lord Shiva and Ganesha’s decapitated head. After seeing the tears in her eyes, Lord Shiva put two and two together. He went to the north and south to find a baby elephant that had wandered off from its mother. He got the elephant’s head and put it on Ganesha’s body giving him his distinct look.
Another story about Ganesha is, once goddess Parvati had a divine fruit wanted by both her sons. Lord Shiva decided that the one who circles the world three times and comes back first would get it as a prize. Upon hearing this, Kartikeya got onto his vehicle, a peacock. He immediately left. However, Ganesha could not pick up speed with his vehicle, a mouse by the name of Mooshak. Then, he realized that he should walk around his parents. After doing so with great devotion, his father, Lord Shiva, asked him why did he circle him instead of the world. He replied that you are the whole world, so he circled him instead.
Many people have wondered why Ganesha has a missing tusk. The story was he was once wandering the forest until he found a brahmin that said that if Ganesha could help him write everything he said in a book. Ganesha said sure and begun writing. He was writing at a lightning speed and was writing everything the Brahmin was saying until the feather he was writing with broke. The brahmin was still saying and was not stopping so Ganesha had no choice but to pull out his tusk and write the rest of the book with his tusk until he was done.