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The term māyā occurs 70 times in Rigveda and around 27 times in the Atharvaveda; and in all these places Yaska, Sayana, Dayananda Saraswati agree the term means Prajñā, jnana-vishesha (specific knowledge). The term Asuri-Maya in the Yajurveda at one place was translated by Uvvat as the "knowledge of the vital air". With regard to the usage of the word Maya in the Rigveda, Radhakrishnan opines it was only used to signify might and power. Maya as the cause of illusion or as the sense of Avidya (lack of knowledge) has never been used in the Vedas. According to Monier Williams, Maya meant wisdom and extraordinary power in an earlier language, but later the word came to mean illusion, fraud, deception, witchcraft, sorcery and magic.
In early Vedic literature, Varuna's supernatural power is called Maya. Though Indra, Agni, and some other gods are said to have Maya, the first Rigvedic phase exclusively connected Maya with Varuna, who is called Mayin and Asura. In the Rig, Indra uses Maya to conquer Vritra.  Monier Williams takes asu to mean life of the spiritual world or departed souls. The association of Varuna with Nritti, death, thus connects Maya with the power of life of the spiritual world or the departed souls. Due to asura's maya, Varuna is said to send rain, create dawn and envelope the night; and with Mitra, Varuna is personified to protect Earth. Varuna found mention as a companion in Indra's exploits and had several Rigvedic verses dedicated to him. In the seventh mandala of Rigveda, many of Varuna's accomplishments are composed exclusively by Vashista; with Vashistas said to be a clan of Varuna-worshippers. Varuna is said to be the brother of Soma and instituted the Rajasuya sacrifice.
However, in the later Rig Vedic phase, Varuna ceased to occupy the position of supremacy and was thence dubbed 'chief of the evil spirits'. The asuras, now dubbed demons, are said to have lost their māyā due to Varuna's power. With the rise of Prajapati, the asura māyā is shared by demons and gods in different forms. Prajapati (and later Vishnu) became identified with the sacrificial rites; and became the sole owner of asuri māyā, that is, white magic which benefits gods and men. The asuras (demons), on the other hand, now wielded black magic to harass the gods (devas). Since Prajapati was considered the father of Varuna, the asuras consecrated Varuna, although Prajapati's rise in the Brahmanic period made Prajapati the overlord of all kinds of magic power. In later literature, Varuna was a keeper of Banasura's cattle and was killed by Krishna who intended to plunder the cattle. Before dying, Varuna is said to have sung a hymn for Krishna before finally yielding to his puranic successor.
In Puranas and Vaishnava theology, māyā is described as one of the nine shaktis of Vishnu. Māyā became associated with sleep; and Vishnu's māyā is sleep which envelopes the world when he awakes to destroy evil. Vishnu, like Indra, is the master of māyā; and māyā envelopes Vishnu's body. The magic creative power, Māyā was always a monopoly of the central Solar God; and was also associated with the early solar prototype of Vishnu in the early Aditya phase.
In Sangam period Tamil literature, Krishna is found as māyon; with other attributed names are such as Mal, Tirumal, Perumal and Mayavan. In the Tamil classics, Durga is referred to by the feminine form of the word, viz., māyol; wherein she is endowed with unlimited creative energy and the great powers of Vishnu, and is hence Vishnu-Maya. As Maha-Maya, she clouds the knowledge of the new born babe bestowing individual ego, ideas of ownership, screening him from wisdom and involving him in pleasures and pain of the transactional world.
In the Atharva texts, Maya is a prominent deity of the Asuras; while in the Yajurveda the Earth goddess is invoked for universal well being and made asuri māyā with offerings. The Yajurveda also describes māyā as an unfathomable plan; and signifies asuri māyā to be reachable through the mind in a mysterious process. In the Aitareya Brahmana Maya is also referred to as Dirghajihvi, hostile to gods and sacrifices, and was killed by Sumitra during an act of purported love making with Indra. According to Johnston, the Gangetic goddess māyiā can be equated with the goddess māyā found in Ashvagosha's Saundarananda. According to V.S Agrawala, the prakrit variants of goddess māyā include mā, māyi and māyiā.
By the time of Upanishads, māyā was beginning to acquire five contexts of meanings -- ritual, metaphysical, epistemological, mythological and magical -- all of which related to enigmatic qualities of life and consciousness of life. While metaphysically and epistemologically, māyā points to the process of mental creation and material creation, the theoretical usage of māyā allowed for contradiction or rejection of practical usages of māyā corresponding to ritual, mythological and magical approaches. Maya [Shakti] as a power was based on observation and experimentation such that orthoprax priests and ascetics used it in ritual practice with the understanding of māyā as control of life's mysteries. This also involved the conclusion that austerities (tapas) can result in the power to control nature, including gods, acquiring objects of desire, including heaven (svarga) and immortality. In the mythological context, māyā was used in the practical sense, such that practices (rituals, austerities, devotion, or a combination of these) gave mortals control over results of the actions (related to karma) and hope for future. 
In some Upanishads, such as the Shvetashvatara Upanishad, māyā is designated prakriti (nature) and owned by Maheshvara, who as māyin is creator of all manifestations and principles. According to P.K. Agrawala, while māyā is found in later day philosophies in the context of illusion, the theory of Maya in upanishadic philosophy has in its background the cult of the goddess māyā; and the acceptance of Mahesvara-Shiva as her spouse represents the inter-mingling of systems and worship forms of these two divinities.
The early works of Sankya do not identify or directly mention the maya doctrine. Early Sankhya does not identify Prakriti as feminine. But the later Samkhyakarika provides a metaphor of Prakriti as a seductive dancer enticing all inactive Purushas (except one Ishvara, the Mahayogin, who remains free and detached) to join her in creating the world; such that the fall into the created world can only be reversed by breaking away from Prakriti using the spiritual discipline of Ishvara, as a model for liberation. Successful yogic liberation would leave Prakriti without dance partners and she returns to an undifferentiated mass.
Vācaspati Miśra's commentary on the Samkhyakarika attacks the Maya doctrine saying "It is not possible to say that the notion of the phenomenal world being real is false, for there is no evidence to contradict it".
The Sankhya dualism view of Purusha and Prakriti was a metaphysical one related to yogic retreat and isolation. However, some puranic writers portrayed prakriti as a feminine power sacralizing the human body, emotions, nature and human relations.  The goddess as prakriti was identified with the creative maya of the vedanta tradition and the powerful shakti of tantricism.  According to J.N.Tiwari:
philosophical basis of the Great Goddess should be traced to a theistic adaptation of Upanishadic Vedantism mixed with the Samkhya conception of Prakriti. As it is, the Goddess is imagined as the Supreme Principle in her own right, as eternally existing, as Supreme Knowledge, as the cause of the bondage and the final liberation of beings, etc. 
In the Brahmavaivarta Purana, Radha is Prakriti and identified with the energy of Brahman; with her being the true form of Brahman and sometimes superior to it. Spiritual qualities (sattvagunas) are considered means of release for Prakriti. The Samkhyakarika says "As the unknowing milk functions for the sake of the nourishment of the calf; so the prakṛti functions for the sake of the release of the puruṣa".
The mystic teachings in Vedanta are centered on a fundamental truth of the universe that cannot be reduced to a concept or word for the ordinary mind to manipulate. Rather, the human experience and mind are themselves a tiny fragment of this truth. In this tradition, no mind-object can be identified as absolute truth, such that one may say, "That's it." So, to keep the mind from attaching to incomplete fragments of reality, a speaker could use this term to indicate that truth is "Not that."
In Vedanta, māyā is to be seen through, like an epiphany (darśana), in order to achieve moksha (liberation of the soul from the cycle of samsara). Ahamkāra (ego-consciousness) and karma are seen as part of the binding forces of māyā. Māyā may be understood as the phenomenal Universe of perceived duality, a lesser reality-lens superimposed on the unity of Brahman. It is said to be created by the divine application of the Lilā (creative energy/material cycle, manifested as a veil—the basis of dualism). The sanskaras of perceived duality perpetuate samsara.
Maya is often translated as "illusion", since our minds construct a subjective experience, which we are in peril of interpreting as reality. Māyā is the principal deity that manifests, perpetuates, and governs the illusion and dream of duality in the phenomenal Universe. For some mystics, this manifestation is real. Each person, each physical object, from the perspective of eternity, is like a brief, disturbed drop of water from an unbounded ocean. The goal of enlightenment is to understand this—more precisely, to experience this: to see that the distinction between the self and the Universe is a false dichotomy. The distinction between consciousness and physical matter, between mind and body (refer bodymind), is the result of an unenlightened perspective.
In Advaita Vedanta philosophy, māyā is the limited, purely physical and mental reality in which our everyday consciousness has become entangled. Māyā is held to be an illusion, a veiling of the true, unitary Self—the Cosmic Spirit also known as Brahman. The concept of māyā was introduced by the ninth-century Hindu philosopher Adi Shankara. He refuses, however, to explain the relationship between Brahman and māyā.
Many philosophies and religions seek to "pierce the veil" of māyā in order to glimpse the transcendent truth from which the illusion of a physical reality springs, drawing from the idea that first came to life in the Hindu stream of Vedanta.
Māyā is a fact in that it is the appearance of phenomena. Since Brahman is the only truth, māyā is true but not the truth, the difference being that the truth is the truth forever while what is true is only true for now. Since māyā causes the material world to be seen, it is true in itself but is "untrue" in comparison to the Brahman. On the other hand, māyā is not false. It is true in itself but untrue in comparison with the absolute truth. In this sense, reality includes māyā and the Brahman. The goal of spiritual enlightenment ought to be to see Brahman and māyā and distinguish between them. Hence, māyā is described as indescribable. Māyā is avyakta and as Parameshashakti has two principal functions: one is to veil Brahman and obscure and conceal it from our consciousness; the other is to present and promulgate the material world and the veil of duality instead of Brahman. The veil of māyā may be pierced, and, with diligence and grace, may be permanently rent. Consider an illusion of a rope being mistaken for a snake in the darkness. Just as this illusion gets destroyed when true knowledge of the rope is perceived, similarly, māyā gets destroyed for a person when they perceive Brahman with transcendental knowledge. A metaphor is also given—when the reflection of Brahman falls on māyā, Brahman appears as God (the Supreme Lord). Pragmatically, where the duality of the world is regarded as true, māyā becomes the divine magical power of the Supreme Lord. māyā is the veritable fabric of duality, and she performs this role at the behest of the Supreme Lord. God is not bound by māyā, just as magicians do not believe the illusions of their own magic.
The following passage is by Sri Shankaracharya:
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One should understand clearly what is "field" and what is "The Knower of this field" in order to understand Maya. For the work of Maya is nothing but to fool us, by showing the "field" or "body" as the self (us) and the "Knower of the field" or the "Soul" as unreal. While the truth is that the self (we) are the "Knower of the field" / "Soul" and the "field" / "body" is apart from us, we merely see this body day to day, as it is born and dying and reborn. (See section end for how to overcome Maya).
Spoken by Krishna to Arjuna on the battlefield of Kurukshetra Bhagavad Gita, Ch. 13, Verse 26:
Wherever a being is born, whether unmoving or moving, know that Arjuna, as born from the union between the field and the knower of the field.
(Purusha is the knower of the field; Prakriti (nature) is the field; Shiva is another name for the knower of the field and Shakti is the field; Spirit is another name for the knower of the field and Matter (Prakriti) is the field; The Knower of the field is also called as Soul where its embodied body is the field;)
Bhagavad Gita, Ch. 13, Verse 30:
Only he who sees that all activities are performed by the body (field), which is created of material nature, and sees that the Self (Knower of the field) does nothing, sees aright.
(The Self (Knower of the field) is the inactive witness.)
Bhagavad Gita, Ch. 18, Verse 61:
Arjuna, God abides in the heart of all creatures, causing them to revolve according to their Karma (Desires) by His illusive power (Māyā) as though mounted on a machine.
Bhagavad Gita, Ch. 7, Verse 25:
(Sri Bagawan Krishna says:)I (Knower of the field) am never manifest to the foolish and ignorant. For them I am covered by My eternal creative potency [yoga-Maya]; and that is why the deluded world knows Me not, Who am unborn and infallible.
Thus Maya is Lord Krishna's potency which he uses upon ignorant people to hide himself as ignorant people do nothing but find fault in the Lord. To overcome Maya and understand the True self and to see Lord Krishna one must have faith and devotion towards Him as stated below.
Bhagavad Gita, Ch. 11, Verse 54:
(Sri Bagawan Krishna says as below after showing His four-armed form to Arjuna:)
My dear Arjuna, only by undivided devotional service can I be understood as I am standing before you, and can thus be seen directly. Only in this way can you (not only see Me but also) enter into the mysteries of My being.
Hence one should have faith and devotion to Lord Krishna in order to understand him and his divine potency - Yogmaya.
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In Hinduism, māyā is also seen as a form of Laksmi, a Divine Goddess. Her most famous explication is seen in the Devi Mahatmyam, where she is known as Mahamāyā. Because of its association with the goddess, Mayā is now a common girl's name in India and amongst the Indian diaspora around the world.
Essentially, Mahāmāyā (great māyā) both blinds us in delusion (moha) and has the power to free us from it. Māyā, superimposed on Brahman, the one divine ground and essence of monist Hinduism, is envisioned as one with Laxmi, Durgā, etc. A great modern (19th century) Hindu sage who often spoke of māyā as being the same as the Shakti principle of Hinduism was Shri Ramakrishna.
In the Hindu scripture Devi Mahātmyam, Mahāmāyā (Great māyā) is said to cover Vishnu's eyes in Yoganidra (divine sleep) during cycles of existence when all is resolved into one. By exhorting Mahamāyā to release her illusory hold on Vishnu, Brahma is able to bring Vishnu to aid him in killing two demons, Madhu and Kaitabh, who have manifested from Vishnu's sleeping form. Sri Ramakrishna Paramahamsa often spoke of Mother māyā and combined deep Hindu allegory with the idea that māyā is a lesser reality that must be overcome so that one is able to realize his or her true Self.
Māyā, in her form as Durga, was called upon when the gods and goddesses were helpless against the attacks of the demon Mahisasura. The combined material energy of all the gods, including Brahma, Vishnu and Shiva, created her. She is thus said to possess the combined material power of all the gods and goddesses. The gods gave her ornaments, weapons, and her bearer, the lion. She was unassailable. She fought a fierce battle against the demon Mahisasura and his huge army. She defeated the demon's army, killed the demon, and hence restored peace and order to the world. Thus She is, even now, the protector of the Universe, which is lying in her lap.
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In Theravada Buddhism, the current expression of Buddhism most closely associated with early Buddhist practice, māyā is the name of the mother of the Buddha. This name may have some symbolic significance given the place of māyā in Indian thought, but it does not seem to have led this tradition to give to the concept of māyā much of a philosophical role. The Pali language of Theravada speaks of distortions (vipallasa) rather than illusion (māyā).
Subsequently, in Mahayana Buddhism, illusion seems to play a somewhat larger role. Here, the magician's illusion exemplifies how people misunderstand themselves and their reality, when we could be free from this confusion. Under the influence of ignorance, we believe objects and persons to be independently real, existing apart from causes and conditions. We fail to perceive them as being empty of a real essence, whereas in fact they exist much like māyā, the magical appearance created by the magician. The magician's illusion may exist and function in the world on the basis of some props, gestures, and incantations, yet the show is illusory. The viewers participate in creating the illusion by misperceiving and drawing false conclusions. Conversely, when appearances arise and are seen as illusory, that is considered more accurate.
Altogether, there are "eight examples of illusion (the Tibetan sgyu ma translates māyā and also other Sanskrit words for illusion): magic, a dream, a bubble, a rainbow, lightning, the moon reflected in water, a mirage, and a city of celestial musicians."  Understanding that what we experience is less substantial than we believe is intended to serve the purpose of liberation from ignorance, fear, and clinging and the attainment of enlightenment as a Buddha completely dedicated to the welfare of all beings.
Depending on the stage of the practitioner, the magical illusion is experienced differently. In the ordinary state, we get attached to our own mental phenomena, believing they are real, like the audience at a magic show gets attached to the illusion of a beautiful lady. At the next level, called actual relative truth, the beautiful lady appears, but the magician does not get attached. Lastly, at the ultimate level, the Buddha is not affected one way or the other by the illusion. Beyond conceptuality, the Buddha is neither attached nor non-attached. This is the middle way of Buddhism, which explicitly refutes the extremes of both eternalism and nihilism.
Nāgārjuna, of the Mahāyāna Mādhyamika (i.e., "Middle Way") school, discusses nirmita, or illusion closely related to māyā. In this example, the illusion is a self-awareness that is, like the magical illusion, mistaken. For Nagarjuna, the self is not the organizing command center of experience, as we might think. Actually, it is just one element combined with other factors and strung together in a sequence of causally connected moments in time. As such, the self is not substantially real, but neither can it be shown to be unreal. The continuum of moments, which we mistakenly understand to be a solid, unchanging self, still performs actions and undergoes their results. "As a magician creates a magical illusion by the force of magic, and the illusion produces another illusion, in the same way the agent is a magical illusion and the action done is the illusion created by another illusion." What we experience may be an illusion, but we are living inside the illusion and bear the fruits of our actions there. We undergo the experiences of the illusion. What we do affects what we experience, so it matters. In this example, Nagarjuna uses the magician's illusion to show that the self is not as real as it thinks, yet, to the extent it is inside the illusion, real enough to warrant respecting the ways of the world.
For the Mahayana Buddhist, the self is māyā like a magic show and so are objects in the world. Vasubandhu's Trisvabhavanirdesa, a Mahayana Yogacara "Mind Only" text, discusses the example of the magician who makes a piece of wood appear as an elephant. The audience is looking at a piece of wood but, under the spell of magic, perceives an elephant instead. Instead of believing in the reality of the illusory elephant, we are invited to recognize that multiple factors are involved in creating that perception, including our involvement in dualistic subjectivity, causes and conditions, and the ultimate beyond duality. Recognizing how these factors combine to create what we perceive ordinarily, ultimate reality appears. Perceiving that the elephant is illusory is akin to seeing through the magical illusion, which reveals the dharmadhatu, or ground of being.
Buddhist Tantra, a further development of the Mahayana, also makes use of the magician's illusion example in yet another way. In the completion stage of Buddhist Tantra, the practitioner takes on the form of a deity in an illusory body (māyādeha), which is like the magician's illusion. It is made of wind, or prana, and is called illusory because it appears only to other yogis who have also attained the illusory body. The illusory body has the markings and signs of a Buddha. There is an impure and a pure illusory body, depending on the stage of the yogi's practice.
The concept that the world is an illusion is controversial in Buddhism. The Buddha does not state that the world is an illusion, but like an illusion. In the Dzogchen tradition the perceived reality is considered literally unreal, in that objects which make-up perceived reality are known as objects within ones mind, and that, as we conceive them, there is no pre-determined object, or assembly of objects in isolation from experience that may be considered the "true" object, or objects. As a prominent contemporary teacher puts it: "In a real sense, all the visions that we see in our lifetime are like a big dream [...]". In this context, the term visions denotes not only visual perceptions, but appearances perceived through all senses, including sounds, smells, tastes and tactile sensations.
|“||The real sky is (knowing) that samsara and nirvana are merely an illusory display.||”|
—Mipham Rinpoche, Quintessential Instructions of Mind, p. 117
Even the illusory nature of apparent phenomena is itself an illusion. Ultimately, the yogi passes beyond a conception of things either existing or not existing, and beyond a conception of either samsara or nirvana. Only then is the yogi abiding in the ultimate reality.
In Sikhism, the world is regarded as both transitory and relatively real. God is viewed as the only reality, but within God exist both conscious souls and nonconscious objects; these created objects are also real. Natural phenomena are real but the effects they generate are unreal. māyā is as the events are real yet māyā is not as the effects are unreal. Consider the following examples. In the moonless night, a rope lying on the ground may be mistaken for a snake. We know that the rope alone is real, not the snake. However, the failure to perceive the rope gives rise to the false perception of the snake. Once the darkness is removed, the rope alone remains; the snake disappears.
In some mythologies the symbol of the snake was associated with money, and māyā in modern Punjabi refers to money. However in the Guru Granth Sahib māyā refers to the "grand illusion" of materialism. From this māyā all other evils are born, but by understanding the nature of māyā a person begins to approach spirituality.
The teachings of the Sikh Gurus push the idea of sewa (selfless service) and simran (prayer, meditation, or remembering one's true death). The depths of these two concepts and the core of Sikhism comes from sangat (congregation): by joining the congregation of true saints one is saved. By contrast, most people are believed to suffer from the false consciousness of materialism, as described in the following extracts from the Guru Granth Sahib:
^ a: From a Proto-Indo-Iranian *māyā, cognate to Avestan māyā with an approximate meaning of "miraculous force", of uncertain etymology, either from a root may- "exchange", or from a root mā- "measure", among other suggestions; Mayrhofer, EWAia (1986-2001), s.v.