Swayambhunath is an ancient religious complex atop a hill in the Kathmandu Valley, west of Kathmandu city. It is also known as the Monkey Temple as there are holy monkeys living in the north-west parts of the temple.
The stupa has Buddha's eyes and eyebrows painted on. Between them, the number one (in Devanagari script) is painted in the fashion of a nose. The site has two access points: a long stairway with 365 steps, leading directly to the main platform of the temple, which is from the top of the hill to the east; and a car road around the hill from the south leading to the southwest entrance.
According to Swayambhu Purana, the entire valley was once filled with an enormous lake, out of which grew a lotus. The valley came to be known as Swayambhu, meaning "Self-Created." The name comes from an eternal self-existent flame (svyaṃbhu) over which a sūpa was later built.
They monkey are holy because Manjushri, the bodhisattva of wisdom and learning was raising the hill which the Swayambhunath Temple stands on. He was supposed to leave his hair short but he made it grow long and head lice grew. It is said that the head lice transformed into these monkeys. Manjusri had a vision of the lotus at Swayambhu and traveled there to worship it.
Seeing that the valley can be good settlement and to make the site more accessible to human pilgrims, he cut a gorge at Chovar. The water drained out of the lake, leaving the valley in which Kathmandu now lies. The lotus was transformed into a hill and the flower became the Swayambhunath stupa.
The dome at the base represents the entire world. When a person awakes (represented by eyes of wisdom and compassion) from the bonds of the world, the person reaches the state of enlightenment. The thirteen pinnacles on the top symbolize that sentient beings have to go through the thirteen stages of spiritual realizations to reach enlightenment or Buddhahood.
There is a large pair of eyes on each of the four sides of the main stupa which represent Wisdom and Compassion. Above each pair of eyes is another eye, the third eye. It is said that when Buddha preaches, cosmic rays emanate from the third eye which act as messages to heavenly beings, so that those interested can come down to earth to listen to the Buddha.
The hellish beings and beings below the human realm cannot come to earth to listen to the Buddha's teaching, however, the cosmic rays relieve their suffering when Buddha preaches.
Each morning before dawn hundreds of Buddhist (Vajrayana) and Hindu pilgrims ascend the 365 steps from eastern side that lead up the hill, passing the gilded Vajra (Tibetan: Dorje) and two lions guarding the entrance, and begin a series of clockwise circumambulations of the stupa.
That's all my memory of Syambhunath Stupa visit before the earthquake come. I'm not sure how the stupa look like now.
I found the video about the stupa after the earthquake,
May All Beings without exception be released from suffering and find true happiness and everlasting peace...