Buddhology is the study of the Buddha or Buddhahood. The term is also used as a synonym for Buddhist Studies, contemporary academic investigation of Buddhism. There are varied and nuanced understandings of the precise nature of a Buddha expressed in the different Buddhist traditions and movements.
Theravada Buddhists base their view of the Buddha on the Pali Canon, which appear to be the oldest surviving Buddhist scriptures. From the accounts contained in the Pali Canon emerges the view that Buddha was a human being — a perfected human being. Buddha was also possessed of all the various supernatural powers, and mastered these to the greatest extent possible (Digha Nikaya 11: Kevatta Sutta). The body and mind of a Buddha (while alive) are impermanent and changing, just like the body and mind of ordinary people. A Buddha does recognize the unchanging nature of the Dharma, which is an eternal principle, and an unconditioned and timeless phenomenon.
When Buddha died at the age of 80, his body and mind both came to an end. After death, the state of Buddha is undefinable (MN 22). A Buddha does, however, definitely not experience rebirth after death, but experiences the attainment of Parinibbana (the ultimate Nirvana). There is thus an end to the life-continuity of rebirths succeeding one-another (this is one of the meanings of samsara).