Nisargadatta Maharaj (from I Am That):
"When you go beyond awareness, there is a state of non-duality, in which there is no cognition, only pure being. In the state of non-duality, all separation ceases."

Ken Wilber:
"Nonduality" means, as the Upanishads put it, "to be freed of the pairs." That is, the great liberation consists in being freed of the pairs of opposites, freed of duality-and finding instead the nondual One Taste that gives rise to both. This is liberation because we cease the impossible, painful dream of spending our entire lives trying to find an up without a down, an inside without an outside, a good without an evil, a pleasure without its inevitable pain.

Adyashanti:
To awaken to the absolute view is profound and transformative, but to awaken from all fixed points of view is the birth of true nonduality.
...
Enlightenment means the end of all division. It is not simply having an occasional experience of unity beyond all division, it is actually being undivided. This is what nonduality truly means. It means there is just One Self, without a difference or gap between the profound revelation of Oneness and the way it is perceived and lived every moment of life. Nonduality means that the inner revelation and the outer expression of the personality are one and the same. So few seem to be interested in the greater implication contained within profound spiritual experiences, because it is the contemplation of these implications which quickly brings to awareness the inner divisions existing within most seekers.

Richard Miller:
Advaita means, "not-two" and reveals the truth that all objects are expressions of unqualified Consciousness and always point back to Awareness, our true nature, the unfathomable Vast-ness-that-we-are. Consciousness and its objects are One, not two. This can never be conceptualized, only intuitively realized. Yana is the pathless "path" we traverse as our misperceptions of separation are healed. This path is not developmental. Separateness is not a case of something that exists becoming non-existent. Our 'self' never exists in the first place except conceptually. The path reveals the non-existence of the 'self' that always was nonexistent. Yoga is the means we utilize in realizing our non-separateness. We investigate all that we take ourself to be (body, senses and mind), and understand That, which we always are Be-ing-unqualified Presence. The body/mind is an expression of Consciousness, and we are That unqualified Consciousness. There is only Consciousness. Our yearning to understand comes from Consciousness. The path we traverse unfolds in Consciousness. The means that we utilize are the tools provided by Consciousness. And That, which we realize is Consciousness. Therefore, the emphasis of Advaitayana Yoga from the beginning, in the middle, and at the end is not on transformation but upon seeing, listening, understanding and welcoming all that is. From the non-dual perspective nothing needs to be changed in order for freedom to be ex-perienced. It takes effort to live our separateness. It takes no effort to be free. This is the final understanding of Advaitayana Yoga.

Bede Griffiths (1997):
"Advaita (nonduality) does not mean "one" in the sense of eliminating all differences. The differences are present in the one in a mysterious way. They are not separated anymore, and yet they are there."

from Andrew Harvey, in "Dialogues With a Modern Mystic"
Andrew Harvey and Mark Matousek:
Advaita is not monism. Advaita means "not-two." We and the universe are not "one": then all distinctions would be destroyed. We are "not-two," intricately interrelated with everything, both separate, unique *and* united. The astonishment of this dance of "not-two" grows slowly as the mind and heart open in divine love and wisdom. Imagine that there was a heap of gold and a skillful smith. The smith made fir trees, geraniums, tables, human beings, lamps. Every object had a different shape, a different purpose and identity but was made of the same thing. Look at the sea. All waves are rising and falling differently, in different rhythms, with different volumes. Some catch the light some do not. You can see the separations between the waves but what you also see quite clearly is that all the waves are water. That is what the knowledge of "not-two" is like. Things retain the separateness which the senses give them, which we use to negotiate this reality, but the illumined mind knows that all things are Brahman, waves of one infinite sea of light. You know, in other words, that you and everything and the light that is at all times manifesting everything are "not-two," and "you" come to exist normally on all levels of the divine creation, and meet "yourself" in all states, events, conditions, beings. This is sahaja, spontaneous negotiation of and union with all dimensions at all moments. Nisargadatta Maharaj explains most lucidly the marvelous transitions to this state: "When the I am myself goes, the I am all comes. When the I am all goes, the I am comes. When even I am goes, Reality alone is and in it every am is preserved and glorified."

It is wonderful that this the most ultimate and holy of all possible experiences in this world, that of unity, of advaita, has to be enjoyed by everyone in their own profound solitude, at that diamond point of solitude at which everyone secretly joins and meets God and each other and all things. This final experience kept for this most sacred and secret moment and is too vast an precious to be ever completely communicated. This is the moment when the created one returns to the source of creation the moment at which all laws, dogmas and techniques that helped the mystic arrive at that diamond point vanish in the silence of return to origin.

Lex Hixon:
"Basically, non-duality is a continual correction of dualistic conceptions as they arise. It's a spontaneous process which, without judgment, playfully erases lines of division as they arise. You can't have a map without lines of division, certainly. Celebrating non-duality is pre-mapping or post-mapping. It doesn't negate mapping, because when you have a good map, there's the paper right behind it, giving it vividness and making it readable. How to get to this conscious state of being the paper? We have to be extremely careful about the language we use here. There are no energetics, no dynamics, no structures in non-duality. These come later. If our structural social forms are consciously rooted in the celebration of non-duality, they can be more energetic, more dynamic, more kind, more insightful."