Advaita Vedanta means, literally, the “end or the goal of the Vedas”. Advaita means, literally, non-duality, and refers to the identity of the Self (Atman) and the Whole (Brahman). The key source texts for all schools of Vedānta are the Upanishads, the Bhagavad Gita and the Brahma Sutras.
The first person to explicitly consolidate the principles of Advaita Vedanta was Adi Shankara (788 CE – 820 CE), an Indian philosopher from Kerala who consolidated the doctrine of Advaita Vedanta. He travelled across India and other parts of South Asia to propagate his philosophy through debates and discourses.
As mentioned on Wikipedia: his works in Sanskrit concern themselves with establishing the doctrine of Advaita (Nondualism). He also established the importance of monastic life as sanctioned in the Upanishads and Brahma Sutra, in a time when the Mimamsa school established strict ritualism and ridiculed monasticism. Shankara represented his works as elaborating on ideas found in the Upanishads, and he wrote copious commentaries on the Vedic Canon (Brahma Sutra, Principal Upanishads and Bhagavad Gita) in support of his thesis. The main opponent in his work is the Mimamsa school of thought, though he also offers some arguments against the views of some other schools like Samkhya and certain schools of Buddhism that he was partly familiar with.
According to Eliot Deutsch and Rohit Dalvi, Advaita Vedanta has been influenced by Buddhism, specifically the Madhyamaka tradition: “In any event a close relationship between the Mahayana schools and Vedanta did exist with the latter borrowing some dialectical techniques, if not specific doctrines, of the former” and also “Gaudapada rather clearly draws from Buddhist philosophical sources for many of his arguments and distinctions and even for the forms and imagery in which these arguments were cast”.
However Advaita, and other traditions of Vedanta, officially base themselves chiefly on the teachings of the Upanishads, a collection of philosophical texts that include Pre-Buddhist, Buddhist era and Post-Buddhist texts. Radhakrishnan in fact considers the Buddha himself to be a part of the philosophical tradition that began with the earliest Chandogya and Brihadaranyaka Upanishads.