What is non-duality in Buddhism?

Buddha rejected the two extremes of existence and non-existence and taught Dependent Origination. As far as I understand Buddha rejected an individual soul or universal soul.

Non-duality in Buddhism is the Mahayana doctrine. Nagarjuna refutes all positive metaphysical theories and views leaving standing only the neutral or 'middle way' theory required for a doctrine of Unity. This denies the fundamentals status of all distinctions and divisions.

Thus Nagarjuna's proof is able to serve as the philosophical foundation of Middle Way Buddhism, Taoism, advaita Vedanta, Sufism and Christian mysticism as presented by Eckhart, Nicolas de Cusa and their like, and by modern books by authors such as Paul Ferrini, Keith Ward and David Bentley Hart. It is the acknowledged foundation for the monumental exposition of Christian teachings in 'A Course in Miracles' and 'A Course in Love'.

Nagarjuna is thought to have constructed his proof in order to address the divergence of views among the sangha of his time. He couldn't have done a more thorough job, but somehow his efforts didn't work. Yet his proof is unassailable and nobody has ever shown that his result is incorrect. He logically proves the non-dual nature of Reality and there is no reason every Buddhist should not accept this proof.

The topic is something of a can of worms since Nagarjuna's logical argument was designed to persuade everybody to agree on a single fundamental doctrine, and naturally this requires that many people change their views. Generally speaking, looking beyond Buddhism to 'mysticism' as a whole, it seems there is a growing consensus and understanding that the principle of non-duality is required for the knowledge claims of the mystics, such that if Reality is not the Unity of which they speak then their self-avowed knowledge would be impossible.

To confirm the endors*m*nt of non-dualism by mystics across the ages is quite easy and it is actually difficult to miss once we know what to look for. But it is a difficult idea and so it takes time to learn what to look for. Thus it is often missed, It is invariably missed by academic philosophers, who rarely know anything of it.

It's a pity we cannot all agree on this since a denial of non-duality weakens the philosophical and intellectual plausibility of the Buddha's teachings and, according to Nagarjuna, renders them incoherent.

Non duality is simply a description of when the psychological barriers between subject and object break down. The experience is characterized by a sense of unity. You might hear the sound of a cat meowing and feel like it’s coming from within your own body. Sound doesn’t come to your ear but rather happens inside an emptiness that has no boundaries. Movement happens in a medium that is stationary, etc.

Advaita in Vedic Hinduism means Non-duality. Parallel to that "Advaya" (अद्वय) is also a Sanskrit word that means "identity, unique, not two, without a second," and typically refers to the two truths doctrine of Mahayana Buddhism, especially Madhyamaka.

Madhyamaka ("Middle way" or "Centrism"; Sanskrit: Madhyamaka, Chinese: 中觀見; pinyin: Zhōngguān Jìan, Tibetan: dbu ma pa) also known as Śūnyavāda (the emptiness doctrine) and Niḥsvabhāvavāda (the no svabhāva doctrine) refers to a tradition of Buddhist philosophy and practice founded by the Indian philosopher Nāgārjuna (c. 150-250 CE). The foundational text of the Mādhyamaka tradition is Nāgārjuna's Mūlamadhyamakakārikā (Root Verses on the Middle Way). More broadly, Madhyamaka also refers to the ultimate nature of phenomena and the realization of this in meditative equipoise. Central to Madhyamaka philosophy is śūnyatā, "emptiness", and this refers to the central idea that dharmas are empty of svabhāva.

Now, Nargarjuna only explained the concept of Buddha's Nirvana in his technical words.

In the Buddhist context, nirvana refers to realization of non-self and emptiness, marking the end of rebirth by stilling the fires that keep the process of rebirth going.

Actually the word "Vaan" means to possess something(like Balvan means who is strong, Dhanvan means who is rich, Purtravan means who has sons) and "Nir" means to reject. Hence, the word Nirvana in a way means to reject all the material things and attributes including mind, body and ego which leads to Sunyata(or emptiness), similar to the concept of Advaya or Advaita, as when every enlightened soul has attained Nirvana(rejection of everthing) into emptiness, they become one in that state. It is called Brahman in Vedas and nothingless is similar to space, in which everything exists but cant be seen. Like in Vedic mathematics, numbers start from 0, similarly everything in the world manifests from 0/Shunyata/emptiness/space and ends in 0 because of death of a person/entire creation.