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Shri Gaudapadacharya

Gaudapada (c. 8th century CE) (also referred as Shri Gaudapadacharya) was a very early guru in the tradition of Advaita Vedanta school of Hindu philosophy. He is traditionally said to have been the grand-guru of the great teacher Adi Shankara,  one of the most important figures in Hindu philosophy and also believed to be the founder of Shri Gaudapadacharya Math.


Dates

There is some dispute about the date of Shankara, but the most probable date is in the 8th century CE, as per the evidence cited by scholars such as Bhandarkar, K. B. Pathak and Deussen. 
Gaudapada is said to have been the teacher of Govinda, who was the teacher of Shankara. Shankara himself affirms this and quotes and refers to Gaudapada as the teacher's teacher who knows the tradition of the Vedānta (sampradāya-vit). Therefore, Gaudapada must have lived and taught during the 7th century CE. 
Order of Acharyas
The following well known Sanskrit Verse among Smarthas provides the list of the early teachers of the Vedanta in their order. 
Nārāyanam Padmabhuvam Vasishtham shaktiæ ca tatputraæ Parāsharam ca |
Vyāsam Shukam Gaudapāda Mahantam Govindam Yogindram athasya shishyam |
Shri Shankarāchārya mathasya Padmapādam ca hastamalakam ca shishyam |
Tam trotakam vartika karamanyan asmad guru-nsantat-amanato ’smi ||
From this verse we can understand that, first teacher being Lord Narayana himself and line of descent from father to son up to Sri Shuka Acharya. FromLord Narayana to Sri Shuka Acharya the line of succession is known as Vamsarsi-Parampara and from Sri Gaudapadcharya starts the descent ofSanyasins and known as Manava-Guru-Sampradaya.
To bifurcate Acharyas according to the Yuga: 
A) In Satya or Krata Yuga
Lord NarayanaLord Sadashiva and Lord Brahma.
B) In Treta Yuga
1) Vasishta Maharishi 2) Shakti Maharishi and 3) Parashara Maharishi.
C) In Dvapara Yuga
1) Veda Vyasa and 2) Sri Shuka Acharya
D) In Kali Yuga
1) Acharyas start with Sri Gaudapada Acharya and followed by Govinda Bhagavatpada charya, Shri Shankarāchārya etc.
Mandukya Karika
The Māṇḍukya Kārikā or the Gauḍapāda Kārikā, also known as the Āgama Śāstra is the earliest available systematic treatise on Advaita Vedānta.  Gaudapada was the author of this text, which is a treatise in verse form on the Mandukya Upanishad, one of the shortest but most profound Upanishads, or mystical Vedas, consisting of just 13 prose sentences. Gaudapada brings out the subtle meanings locked in these mantras through his work.
The Gaudapadiya Karika is divided into four chapters. The first chapter - Agama, or Agama Prakarana - explains the text of the Mandukya Upanishad and Gaudapada shows that Advaita is supported by the shruti and reason. The second chapter - Vaitathya Prakarana - is concerned primarily with rationally proving the unreality of the phenomenal world characterized by its duality and opposition, on the cessation of which non-duality is attained. Lest by a similar process of arguments reality itself should be negated, the third chapter - Adavaita Prakarana - establishes non-duality and the fourth chapter - Alatasanti Prakarana - quite distinct from the other chapters with its Mahayana Buddhist style of dialectic explains the relativity of our phenomenal experience and establishes the Atman or soul as the only reality underlying the phenomenal existence. He shows the deepest respect for the Buddha whom he salutes repeatedly, and quotes freely fromVaasubandhu and Nagarjuna. 
Chapter One: Traditional Doctrine (Agama)
The Self manifests itself in three forms : as vishva in jagrat or the waking state, as taijasa in svapna or the dream state and as praajna in sushupti or deep sleep. As, vishva it has consciousness of the outside world and enjoys gross objects. As taijasa it has consciousness of the mental states and enjoys internal or dream objects. As prajna it is without distinctions, resides in heart and enjoys bliss. A person who understands these three forms of self is not affected even if he enjoys them. There is a fourth state of Self, called turiya. Turiya is without duality, all pervading, unchanging and is a remover of sorrow. Both prajna and turiya are non-dual, but turiya knows no sleep or ignorance and being self luminous consciousness is all seeing. "Sleep" visits individual (jiva) because of Maya and when jiva awakens it experiences turiya. 
Chapter Two: Unreality (Vaitathya)
The reasoning in this chapter is in consonance with reasoning in Brihadaranyaka Upanishad. The states of waking and dream are both identical since their objects are alike unreal because any object nonexistent in the beginning and end is nonexistent in middle too. Besides, a dreamer believes those objects which are external to him as real and those that are internal to him as unreal, though both are unreal. Likewise, in waking state both external and internal objects are equally unreal. External objects which appear to be fixed in time and internal objects which appear to be fleeting are both created by the Self through its own Maya.[7]
There is no dissolution, no origination, none in bondage, none possessed of the means of liberation, none desirous of liberation, and none liberated. This is the ultimate truth. — Verse 2.32, Mandukya Karika. 
Chapter Three: Nonduality (Advaita)
In this chapter, the author tries to show how non-duality can give rise to apparent duality. To this end he gives the analogy of space and jars. Self is like space and the jivas are like space in jars. Just as space is enclosed in a jar, so is the Self manifested as Jivas. When the jar is destroyed the space in the jar merges into space so likewise, are jivas merged into the Self. Spaces in jars may differ in form, function and name, but still there's no difference in space. Likewise though the jivas may differ in form, function and name, still there's no difference in the Self. Just as the space in the jar is neither the transformation nor a modification nor a part of the space, the jiva too is neither the transformation nor a modification nor a part of the Self. Creation from existence (sat) or from non-existence (asat) are both unreasonable positions since, no creation takes place at all, because immortal Self can never become mortal. 
Asparsha Yoga
Jnana or awareness without conceptual constructions is declared to be Brahman. This awareness is unborn, without sleep or dream, without name and form and is omniscient. When there are no thoughts about objects, awareness rests in itself and attains equanimity. This is called contactless concentration or asparsha yoga and even the yogis are afraid of it. 
That highest Bliss exists in one’s own Self. It is calm, identical with liberation, indescribable, and unborn. Since It is one with the unborn knowable (Brahman), the knowers of Brahman speak of It as the Omniscient. No Jiva (individual), whichsoever, is born. It has no cause (of birth). This is the highest Truth where nothing is born whatsoever. — Verse 3.47-48, Mandukya Karika. 
Chapter Four: The Peace of The Firebrand (Alatasanti)
Gaudapada refutes Sankhya's theory of causality i.e. cause itself is born as effect. He rebuts this by arguing that Sankhya cannot consistently maintain that effect is born and different from cause and nevertheless unborn and eternal. Besides, there is no example to substantiate this theory. Therefore, Gaudapada proposes the theory of Ajativada or non-origination. Ajativada holds that awareness never touches objects or appearances of objects because both objects and appearances are unreal. Moreover, Ajativada is proved by the reasoning that one who believes in origination cannot maintain that the world (Samsara) is beginningless and has an end and that liberation has a beginning and no end, because something that is by nature unborn cannot be born and something which is born must have an end. The consciousness therefore, is only reality but appears as objects like a burning stick swung about appears to be continuous. Our attachment to unreality makes the duality exist from an empirical point of view though, from a highest standpoint objects are nonexistent and unborn Self exists free from fear and sorrow. 
Epistemics of Gaudapada
Gaudapada's karika on the Mandukya Upanisad is an example of the rational epistemics of reality. His rational arguments prove the irrationality of experience. The experience of varied consciousness-states, for instance, proves that none of them can be considered to be real. Gaudapada's portrayal of maya as real yet non-dual in his example of the firebrand attempts to provide a cosmological answer without totally avoiding the empirical dimension.
Other works by Gaudapadacharya
  • Durga Saptashati Tika - Classification of the various chapters of the saptashati
  • Uttara Gita Bhashya
  • Subhagodaya Stuti