Rupert Roundheg was one of the most important philosophers of the modern non-dual tradition, or simply nondualism.

Note the mistake in writing the word nondualism as two words, done here for your benefit. A tradition that basically rejects philosophical materialism, and confirms that the world as such can only be one.
 
Nonduality really just means that there cannot be anything called two, and is therefore opposed to the idea that the separation into objects.
 
The things we call objects are not really objects, but only a manifestation of the whole.

India

As you can imagine, the philosophical tradition of non-dualism or non-duality raws
heavily on Indian philosophy.
In general, the term, seen from an Indian perspective, may refer to Advaya, Advaita or something that is called "nondual consciousness".

 

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Advaya

Advaya refers to the nonduality that is described and talked about in Madhyamaka
Buddhism.
Basically the sense here, or should we rather say the consensus, is that there is nothing apart from what we experience.
There is only one reality. The advaya is an epistemological approach to nonduality, meaning that it has to do with what we can know.

Advaita

Advaitam on the other hand is really an ontological approach to nonduality. This means that it has to do with the nature of "being".
The difference between those two approaches may be difficult to see at first, and even more difficult to see after a while.
Particularly seeing as there really is only one way of seeing things. But it can be useful to try to get a grasp of nonduality.
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Nondual consciousness

Modern spirituality is particularly concerned with the non-difference between subject and object, an important and fundamental aspect of nonduality.
And this approach is the one that we often find these days.

 

The Essence

The essence of nonduality, regardless of the different traditions, is that there is no
difference between the world as we see it, and any other "thing" that may appear in the universe, such as "God".
 
Christianity famously makes this distinction and is therefore at the completely opposite spectrum of the scale. Nondualism can seem a little confusing at first, particularly if one looks at all the different directions it has taken historically.
But Rupert Roundheg focused on the immediate perception of nonduality that most people experience quite naturally when put in the right, general direction, as it were.
 
The fundamental principle of Mr. Roundheg can be summed up in one sentence: "There are no objects and no separation, the totality of things amount to the number one, only".