Dualism to non-dualism

Deep Hindu Philosophy is based on the premise that there is only one absolute and ultimate truth – Brahman – Universal Consciousness and no other one. The universal consciousness along with Souls, the individual consciousness and Matter form an organic whole of the Universe. In the context of creation of the world, the doctrines of dualism and non-dualism are based on differentiation and non-differentiation of three eternals viz. Universal Consciousness (Brahman), Souls (Atman) and World (Jagat).
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Based on physical perception, we decide that the various objects are indeed different. This kind of differentiation is “Duality or Dvaita”. Duality is the foundation of all the actions and worship. According to Dvaita, the world is real. God is the creator of the world. According to Advaita, all the different elements have their origin from same energy. Single energy or Universal consciousness is beyond the reach of the sense organs. Brahman is the one and only reality and everything else is a mere appearance, projection, formation or illusion. Modern science is approaching nearer and nearer to Advaita thought.
The spiritual journey need to be from dualism to non-dualism. The start of the journey is change first in external behaviour i.e., behaving with others as we desire and then internally feeling no differentiation for living beings as entire world is appearance of universal consciousness or almighty. Pains gradually reduces as differentiation diminishes. So, non-dualism brings happiness and ultimately moksha. 
The interactions of the three are variously expounded in Hindu Scriptures & philosophies.
Philosophers of Dualism–Non-Dualism
Duality is the phenomenon of the world. Dualism or differentiation among Nirgun Brahman (universal consciousness, Ishwar), Atman (jiva, individual consciousness) and Jagat (material world) is variously postulated by Hindu philosophers as under –

1. Dvaita – (Madhvacharaya’s Dvait Darshan, 1294 – 1317 AD, he wrote Purnapragya Bhashya) - According to Dvaita, Universe and Jiva are separate from Brahman. All these three elements (Jiva, world and Brahman) are real and different (द्वैत) from each other. There are five types of difference described between 1. Jiva-Ishwar, 2. Jiva-Jiva, 3. Jiva-Jagat, 4. Ishwar-Jagat and 5. Jagat-Jagat.
2. Dvaita-Advait (Nimbarkacharya’s Dvaita-advait, 1028 – 1125AD, he (wrote Vedanta Parijat) - He believed in three eternal realities – Brahman, Jiva and Jagat. Jiva and Brahman can be considered different and also non-different. Brahman is efficient cause of material world. Jiva is Knower, the doer and the experiencer. Brahman is Controller, filler and witness.
3. Shusha Dvait – (Vallabhacharaya’s Shuddha davit, 1479 – 1532, wrote Anu Bhashya) – According to Suddhadvaita, Brahman is the cause for Universe. Maya is not unreal but it is shakti (energy) of Brahman. Jiva is not different from Brahman. Jiva and world emanate from Brahman and conceal/absorb in Brahman.
4. Vishisht Advait – (Ramanujacharya’s Vishishtadvait, 1017 – 1137 AD, he wrote Shri Bhashya) - It is known as qualified non-dualism as it asserts the non-duality of Jiva and Brahman in qualified way i.e., Jiva and Paramatma don’t exist differently - Parmatama always dwells inside Jiva - both can't exist separately. But Jiva and Parmatama are (not same) different.
5. Achintya Bhedabheda - According to Chaitanya Mahaprabhu, Brahman is simultaneously one with and different from his creation. The relationship between Brahman and Jiva is like Sun and Sunshine. Qualitatively the Sun and the Sunshine are not different, but as quantities they are very different.
6. Shankar’s Advait Vedant (788 – 820 AD) of Non-Dualism means that Brahman is the one and only reality and everything else is a mere appearance, projection, formation or illusion. Universal consciousness’s manifestation as plurality of Beings / objects is known to us as duality. But when the individual souls’ merges with cosmic soul (Parmatama) and becomes the ‘Advaitic Brahman’.

 
Advaita on the other had says that action-free, attribute-less “Nirgun Brahman” alone appears to exist as the active attribute-full Ishvara and conducts the business of the world through Maya.  According to Advaita, there is only one absolute and ultimate truth - Brahman. ब्रह्म सत्यं जगत् मिथ्या which means only Brahman is real and universe is unreal. Universe is appeared/realize due to ignorance (अज्ञान/अविद्या) only [Snake & Rope Analogy], it is unreal and just like dream. After attaining the jnana and satya universe/world doesn't exist.  वो ब्रह्मैव नापरः which means ultimately there is no difference between Jiva (Ataman) and Brahman. The individuality of soul is also due to ignorance and after attaining jnana the non-duality (अद्वैत) of Ataman and Brahman is realized. Advaita emphasise/insist on self-realization/jnana (आत्मज्ञान)
Shrimad Bhagavad Gita
Shrimad Bhagavad Gita has expounded that Supreme Brahman has two concepts viz. Nirguna and Saguna. Nirguna Brahman is formless, without attributes or quality. Saguna Brahman, in contrast, was envisioned and developed as with form, attributes and quality.
Vedas
Vedas are dualistic in their impact. But the Vedas talk of non-dualism or Advaita at some places in the Samhitas and extensively in the concluding part, namely the Upanishads. It is concluded that Vedas first postulated Dvaita which is already known to us in our daily experience and later talk of Advaita which is not known to us but seek to establish. Just as the flower appears first and then it drops off leaving the fruit in position, first we have Dvaita and later leave it, and comes over to Advaita.
Shiva Purana
As per Shiva Purana, the manifest form of the formless Being is Shiva. Shiva then created the physical form Shakti from his body. This Shakti is called by various names - Pradhana, Prakriti, Maya, Para. Shakti is the mother of Buddhi Tattva (The cosmic Intelligence).
Kapila’s Samkhya Darshan
Maharishi Kapil propounded Samkhya Darshan wherein he postulated that Prakriti is root of material forms and is not produced. From Prakriti, Mahat (intellect) is produced which in turn produces ego. From ego manas (mind), five subtle elements or tanmatra, arises and they in turn produces five gross elements, five organs (instruments) of senses or perception and five organs of actions.  Other than Prakriti is Jiva (Soul, Purusha). These are 23 elements. Kapil discovered that when the unconscious Prakriti comes in contact with the intelligent conscious Purusha, evolution of the universe begins. Purusha is pure consciousness absolute, eternal and subject to no change.  Samkhya believes in dualism i.e. the creation is by Prakriti and Jiva. “The Purusha (Atma) is mere knowledge without any indulgence in activity. Prakriti is mere activity but without knowledge (Jnana) or life and animation, (Jiva Chaitanya). Such is the clear-cut differentiation, without explaining how it is possible for the Jada (inanimate matter) to transform itself into the other Tatvas. The only explanation offered is that the presence of the Purusha (Jiva Chaitanya) is responsible for such mutations of the Jada.
 
Mandukya Upanishad
Mandukya Upanishad has beautifully explained dualism and non-dualism by four aspects of Atman - Waking, Dreaming, Deep Sleep and Turiya. During waking state, we perceive differentiation between self and rest of the world. consciousness is turned outward to the external world and operates through its seven instruments (five gross elements, individuation & flow of energy) and nineteen channels (four antahkaran, five Vayu, five sense organs & five organs of action) it experiences the gross objects of the phenomenal world. During the dreaming state, consciousness is turned towards the inner world. It also operates through seven instruments and nineteen channels, which engage the subtle objects of the mental realm. During deep Sleep state, there is neither the desire for any gross or subtle object, nor any dream sequences. During Turiya, consciousness is neither turned outward nor inward; it is beyond both cognition and the absence of cognition. This is the real Self.
 
Patanjali’s Yoga Darshan
Patanjali’s Yoga Darshan’ eight limb is Samadhi which leads to Moksha (loosing dual state). Samadhi is the state, when the mind remains for long time as non-attached, afflictions decay which lead to moksha. Samadhi has four stages viz. Savitarka (mind still active), Nirvitarka, Savichar and Nirvichar. On attaining excellence in Nirvichar Samadhi, one becomes pure and witness Brahman.  In all these samadhis, because of the connection with the prakriti—the seed from which everything originates remains i.e. dualism remains. In Nirvichar samadhi you have a separate experience wherein the mind loses all its limitation and it is filled with a new light and all past impressions are completely wiped out. But when you come back, you realize that you were in a higher state so that impression is still there. When even that impression is lost, you are in Nirbija samadhi. Once you go into Nirbija samadhi, there is no coming back. In this seedless state of Nirbija samadhi.
 
Prayers for universal well-being believing Non-Dualism -

1. There is a universal prayer in ancient Hindu texts -

In Sanskrit - “ॐ सर्वे भवन्तु सुखिनः सर्वे सन्तु निरामयाः । सर्वे भद्राणि पश्यन्तु मा कश्चिद्दुःखभाग्भवेत् । ॐ शान्तिः शान्तिः शान्तिः ॥ “
In English - Om May all be happy, may all be free from illness, may all see what is auspicious, may no-one suffer. Means – if all will be happy, we shall be automatically happy. Om Peace, Peace, Peace.

1. Another philosophical thought is on universal peace -

In Sanskrit - अयं निजः परो वेति गणना लघुचेतसाम्। उदारचरितानां तु वसुधैव कुटुम्बकम्॥
In English - or those whose heart is big, the whole earth is family and for those whose heart is small, they think it is their own, it is alien.