Buddha had renounced his luxurious life, left his palace and became wandering ascetic and spiritual teacher.
Buddha is one of the greatest and most influential personalities of all time. He is a highly revered deity all over the world.
Is he avatar of Vishnu or of Lord Shiva?
By some sources, Buddha is considered as an incarnation of Lord Vishnu. An unconventional incarnation of the supreme lord.
Why is he not mentioned in scriptures like the Bhagavad Gita?
Bhagvad Gita was composed long before the birth of Buddha. So He is not mentioned in the holy scripture. If Buddha had been born before the composition of the Bhagavad Gita, then he would definitely have been mentioned in the Gita.