Māndūkya Upanishad is the shortest of the Upanishads - the scriptures of Hindu Vedanta. It is in prose, consisting of twelve verses expounding the mystic syllable Aum, the three psychological states of waking, dreaming and sleeping, and the transcendent fourth state of illumination.
This Upanishad has been greatly extolled. The Muktikopanishad, which talks about all other Upanishads, says that the Māndūkya Upanishad alone will be enough for the salvation. According to Dr.Sardar Vallabhbhai Patel  it contains the fundamental approach to reality.
About the Upanishad
The name literally means the Scripture of Frog. However, the commentators including Gaudapada and Sankara did not touch upon to explain the name. Let us examine some aspects of the name of the Upanishad, which helps us to understand the Vedichistory behind the Upanishad:
1.Some attribute the Upanishad to a sage called Manduka. Manduka means son of "Manduki" and a seer with this metronymic is mentioned in the Brihadaranyaka Upanishad along with the Mandukeyas, his disciples. The Mandukeyas figure in the Bhagavata purana as the receivers of a branch of the Rig Veda from Indra. This group of seers also figures in the Rig Veda itself: their hymns are mostly connected with lingustics, for example Hrsva (short) Mandakeya, a vedic seer who proposed semi vowels. A text on the etymology of Vedas with the name "Manduki Shiksha" deals with the notes of the musical scale. There are more than one Mandukas, since Manduka is a gotra belonging to Asuric Brahmins. (Bhargavas)
2. Connection with Varuna It is said Varuna, the Lord of Cosmic waters, has taken the form of a frog to preach this Upanishad. This story makes it more interesting since there is a hymn called Toad Hymn (manduka sukta) in the Rgveda, which is ostensibly an ode to the arrival of monsoons. But the cosmological significance of the hymn is yet to be unraveled. The connection between the hymn and the Upanishad, in terms of cosmological significance, may be an interesting point to search for. This assertion finds more support since Varuna is an Asuric God and lends himself to the ancestries of more than one Asuric gotra.
3. Manduka is also a type of yoga - a "particular kind of abstract meditation in which an ascetic sits motionless like a frog". Mandukasana is one of the asanas (postures) described in yoga. Seemingly hard to practice. Mandukasana is one of the 32 asanas(postures) described in yoga. Possibly the Upanishad, which is connected with meaning of Aum, which is essentially an Object of Meditation, has been named after Manduka to indicate the yoga aspect of the Aum.
For the very reason that it explains the esoteric meaning of the fundamental syllable Aum of vedic spiritual tradition, the Upanishad has been extolled greatly. The Muktikopanishad, which talks about all other Upanishads, says that if a person cannot afford to study all the hundred and eight Upanishads, it will be enough to read just the Māndūkya Upanishad. According to Dr.S. Radhakrishnan, in this Upanishad we find the fundamental approach to the attainment of reality by the road of introversion and ascent from the sensible and changing, cleansing the mind of thoughts, feelings and wishes related to the material, relative world, and reaching the soul which, being spiritual and having an absolute nature as the Lord, is the only one that can perceive Him, Who is also absolute and spiritual, and cannot be perceived with material relative senses.
Exposition of the Upanishad
The Upanishad starts with the assertion that this universe is immersed in brahman, and this universe is brahman. The purusha - loosely translated as consciousness - who is "experiencing" this universe has four components, or, as said in the Upanishad, "parts". The first one is that which experiences the physical world, called Vaiswanara ("Man of the Universe" or "Man of this Universe"). He is said to be residing in the mental state called "Jagra" or wakefulness, and is outward-looking. The second one is that which experiences the dreams, called "Teijasa" ("Man of Light" or "The illuminated Man"), who resides in the dreaming state called "swapna" or dreaming, and is inward looking. The third one is that which experiences nothing, when the person is in deep sleep, and is nowhere-looking. Consciousness keeps on shuttling among these three states, at any time being in only one of these three states.
The Upanishad then states that there exists a fourth state that underlies the above states. The part of purusha that experiences this fourth state is called "Turiya". In this state, the person is not in the physical or dream world, but not in deep sleep either. In deep sleep, one is neither conscious of himself nor of the universe he is existing in; but in the fourth state, a person will be well aware of himself and his universe, even though he will not have the benefit of organs of knowledge (eye, ears, etc.) or the organs of action (hands, feet, etc.). He can be said to be everywhere-looking.
The Upanishad then expounds the sacred syllable aum.
Aum in the Mandukya Upanishad
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There are three mātrās ("letters", syllabic instants in prosody) in the word aum : ‘a’, ‘u’ and ‘m’. The ‘a’ stands for the state of wakefulness, where we experience externally through our mind and sense organs. The ‘u’ stands for the dream state, in which inward experiences are available. In the state of deep sleep, represented by the sound ‘m’, there is no desire and consciousness is gathered in upon itself.
But there is a fourth, transcendent state, that of one "who is neither inwardly nor outwardly aware, nor both inward and outward, nor with consciousness infolded on itself.... who is unseen and ineffable, ungraspable, featureless, unthinkable and unnameable" The fourth state (turīya avasthā) corresponds to silence as the other three correspond to AUM. It is the substratum of the other three states.
Commentary by Gaudapada
The first extant commentary on this Upanishad was written by Gaudapada, before the time of Adi Shankara. This commentary, called the Māndūkya-kārikā, is the earliest known systematic exposition of advaita Vedanta. When Shankara wrote his commentary on Māndūkya Upanishad he merged the Kārikā of Gaudapada with the Upanishad and wrote a commentary on the Kārikā also.
Gaudapada deals with perception, idealism, causality, truth, and reality. In the fourth state of consciousness - turiya - the mind is not simply withdrawn from the objects but becomes one with Brahman. In both deep sleep and transcendental consciousness there is no consciousness of objects but the objective consciousness is present in an unmanifested 'seed' form in deep sleep, while it is transcended in turīya. Specifically, if one identifies the wordless state with turīya and meditates, one realizes the true self and 'there is no return to the sphere of empirical life'.
- S. Radhakrishnan. The Principal Upanishads. George Allen and Unwin. 1969
- Phonology: Critical Concepts by Charles W. Kreidler
- Swami Nikhilananda: Mandukyopanishad with Gaudapada’s Karika and Sankara’s Commentary. Shri Ramakrishna Ashrama, Mysore. Sixth edn. 1974
- Eight Upanishads. Vol.2. With the commentary of Sankaracharya, Tr. By Swami Gambhirananda. Advaita Ashrama, Calcutta, 1990.
- V. Krishnamurthy. Essentials of Hinduism. Narosa Publishing House, New Delhi. 1989
- Swami Rama. Enlightenment Without God [commentary on Mandukya Upanishad]. Himalayan International Institute of Yoga Science and Philosophy, 1982.
- Sri Aurobindo, The Upanishads . Sri Aurobindo Ashram, Pondicherry. 1972.