Panchakoshas (पंचकोश, the five sheaths), are the layers of body that seemingly cover the Atman (Self or Consciousness). The Tvam ("Thou") padartha of the Mahavakya Tat Tvam Asi is determined by the analysis of Panchakoshas that are not the atman. Panchakoshas are discussed in the Brahmanandavalli Chapter of Taittiriya Upanishad which is a part of the Taittiriya Samhita of the Krishna Yajur Veda and in which particular chapter is discussed ways and means to achieve Brahman. It gives a detailed description of the dimensions of human personality or the dimensions of the Self.
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What is Atman?
The Sruti declares that human birth, by divine grace, is meant to strive to know and understand the atman. The knowledge and understanding of the atman invariably results in Jiwanmukti i.e. Moksha or "Spiritual liberation". Spiritual Liberation is of the nature of bliss in which there is complete negation of all sorrow, it does not arise by mere study of sastras, sacrifice to gods, performance of karmas and meditation on the divinities, these acts do not result in the knowledge of the unity of atman. Atman is Brahman who is of the nature of satyam, jnanam and anantam, and the knower of Brahman becomes Brahman. Knowledge is gained after renouncing attachment to all sense-objects and all actions, for one's body, that harbours the mind that makes for bondage and is not the atman. The Atman is the substratum of the consciousness of "I".
Anatman means not-self or non-self. Anatman is everything that is not Atman. All objects of consciousness are called Anatman, including the mind and the ego.
The samsara is the vast turbulent ocean which is the embodiment of avidya and its effects that cannot be crossed without the aid of perfect wisdom; the samsara is the anatman. By non-realisation of the true nature of the atman, the atman is mistaken as the karana sarira ("causal body"), suksma sarira ("subtle body") and sthula sarira ("gross body") which bodies constitute the anatman. For a person who is unaware of the atman there is no other go except to do karmas intended for purification of the mind. 
What are Panchakoshas?
The Panchakoshas are listed as follows -
- Annamaya Kosha - The food sheath
- Pranamaya Kosha - The vital energy or breath sheath
- Manomaya Kosha - The mind sheath
- Vijnanamaya Kosha - The intellect sheath
- Ananadamaya Kosha - The bliss sheath
Panchakoshas are divided in three bodies -
- The gross body sthula sarira - made up of physical matter. This body consists of Annamaya kosha and Pranamaya Kosha.
- the subtle body suksma sarira - This body consists of Manomaya Kosha and Vijanamaya Kosha.
- the causal body karana sarira - This body consists of Ananadamaya Kosha.
The atman is behind the Panchakoshas. The Sathula sarira is the Annamayakosha (food-ful, consisting of the gross body). The Suksma sarira is made up of the Pranamayakosha (energy-ful, the subtle body), the Manomayakosha (instinctive, the perceptual body) and the Vigyanamayakosha (cognitive, the conscious body). The Karana sarira is the Anandamayakosha (blissful, the transcendental body).  The Sruti insists upon elimination of these five sheaths of the sariras. The doctrine of Panchkoshas represents the hierarchy of human values and is held to be a useful springboard for a modern scientific understanding of cosmology and evolution.
Anna means matter, annam literally means food; Taittiriya Upanishad calls food the medicament of all.  The gross body which is matter-born and matter sustained and transient and subject to perception is the Annamayakosha whose origin is food eaten by parents. It is visible, dependent and impure. It is not the atman because it did not exist before its origination and ceases to exist once it is destroyed. It is subject to origination and destruction every moment. It is the anatman because it is not in the beginning and at the end, is non-existent also in the present. It does not know itself. The deluded mind that does not inquire considers his atman to be this body or kosha. Such a person cannot enjoy bliss. 
Pranamayakosha, separate from and subtler than Annamayakosha, pertains to the Sukshma sarira, it is the sheath of the vital airs completely enclosing and filling the Annamayakosha. The Prana in combination with the five organs of action constitutes the Pranamayakosha. The Annamayakosha is an effect of the Pranamayakosha.  The Annamayakosha gets life by the Prana entering into it and engages in all kinds of action. Prana is the life of beings and the Universal life. Whatever happens in the Annamayakosha is wrongly identified as belonging to the atman by reason of its being pervaded by the Pranamayakosha which is effect of Vayu, and totally unaware and dependent. 
Manomayakosha belongs to the Suksma sarira. It is the "self" having Pranamayakosha as its body.  The organs of knowledge and the mind form this kosha which is the cause of the sense of the "I" and of the "mine" and of the varying conceptions. It creates difference of names etc., because organs of knowledge are dependent on and determined by the mind which is of the nature of determination and doubt. It is powerful because bondage and liberation depend on the mind which producing attachment binds a person and which by creating aversion for them liberates them from that self-made bondage. It pervades the Pranamayakosha. It is the sacrificial fire, the five organs are the priests who pour into this fire the oblations of sense-objects, which fire fuelled by various vasanas burns out the world created and expanded by the mind that when fouled by rajas ("projection") and tamas ("concealment") superimposes the samsara but when free of rajas and tamas can bring about the state of being established in Brahman. 
The word Vijnana means Knowledge. This layer is made of the intellect and knowledge. This is the part of mind that makes decisions, and takes ownership of action and becomes an ego.
Vijnanamaya kosha also belongs to the Suksma sarira and pervades the Manomayakosha that pervades the Pranamayakosha which pervades the Annamayakosha. Buddhi with its organs of knowledge and its actions having the characteristics of an agent is the Vigyanakosha, the cause of samsara. It has the power of reflection of the chaitanya which it accompanies as a modification of Prakrti (avidya) and characterised by knowledge and action and always identified with the body, organs etc. This kosha is endowed with jnana and to it belong the waking and dream states and the experiences of joy and sorrow. Being very luminous in close proximity of the Paramatman deluded by which upadhi it is subject to samsara, this atman which is compacted of vigyanana and shining in the heart near the pranas being immutable becomes a doer and enjoyer in the midst of the upadhis. Its "jivabhava-existential-character" i.e. Jivahood, persists so long as there is delusion as it is born of mithyajnana. Though avidya is beginningless it is not eternal. 
Ananda means bliss. This is the bliss of the Atman. This bliss is experienced when we fall into deep sleep.
Anandamaya kosha is the last layer and it is the closest layer to the Atman. It is a modification of avidya and appears as a reflection of the atman compacted of absolute bliss. It is fully manifested in the dreamless deep sleep. It is not the atman because it is connected with upadhis ("limitations") and a modification of Prakrti as an effect of good deeds. 
Atman can be identified only by negation of the anatman. The Panchkoshas are anatman that hide the atman, these koshas or sheaths are required to be systematically removed. Their removal brings to fore a void which void is also required to be removed. After removal of the five sheaths and the resultant void through the process of negation, what remains is the Atman; and then the non-existence of all the modifications beginning with the ahamkara is self-witnessed, the self that witnesses is itself the supreme Self.  These five sheaths envelop the atman or "soul". The Vedanta conceives the expression of the gross universe possible by traversing through all these stages of emanation from the cloud of Maya covering the face of Brahman to Sthula bhutas or gross matter with all its multifarious aspect including gross energy.  Badarayana, drawing attention to Pāṇini’s grammar (V.iv.21), explains that the suffix mayat as in Annamaya (made of food), Pranamaya (made of vital air) etc., besides conveying the meaning "made of" has also the sense of abundance and plenitude as well for which reason it is repeatedly said - Brahman is the Blissful (Anandamaya) Self.
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