Maya can never be supreme as it operates only in Vyavaharik level. According to Advaita there are three levels of reality:
- Paramarthika Satyam
- Vyavaharik Satyam
- Pratibhasik Satyam
In Vyavaharika level the world exists like real, even if one says that everything is Maya or Brahman or Avidya still he/she has to function as per rules of the world like one has to eat food, and in food also one can't eat stone (saying that both food and stone are differentiation of the same thing). Regarding this we find quotes of Adi Shankara like:
In Brihadaranya Upanishad Bhasya 3.5.1 Adi Shankara says:
सर्ववादिनामपि अपरिहार्य: परमार्थ-संव्यवहारकृतो व्यवहारः ।
In fact, all schools must admit the existence or non-existence of the phenomenal world according as it is viewed from the relative or the absolute standpoint.
Similarly in the Taittariya Upanishad Bhasya 2.6 also Shankara mentions about Paramarthika and Vyavaharika levels of reality. On its commentary by Sureshwaracharya also he mentions the same. This site gives a passage written by an Advaitin AchyutaKrishnananda Tirtha which also specifically mentions the terms Paramarthika, Vyavaharika and Pratibhasika type of reality.
This is the absolute reality. In this level neither Ishwara nor Maya exists. Only Brahman exists in Sat-Chit-Aananda Swarupa. Here Sat means pure existence of Brahman, Chit means pure consciousness of Brahman and Aananda means infinite blissfull state of Brahman. There is neither any creation nor any destruction in this state. Just Brahman exists in Satchitaananda form.
This type of reality is called Ishwara Shristi. This is the reality at that level when universe is covered by Maya of Ishwara. Maya is the potential energy of Ishwara. For eg. We see Mirage in desert. That is illusion. We know it but we can't remove it by knowing it. We can just understand that it is illusion. Similar is the level of Vyavaharika Satyam. We can only understand Maya of Ishwara.
This type of reality is also known as Jeeva Shristi. We ourselves create these types of reality in our mind. For eg. In our dreams. Dream world is created by ourselves. Another example is seeing rope as snake in dim light. These type of illusions are instantaneously removed after knowing the truth. But illusions of Vyavaharik level can't be removed,we can only understand it (ie. Mirage still exists even if we have knowledge that it is an illusion)
Ishwara himselfs creates this Universe by the power of Maya. Ishwara does so because creating is his nature. Ishwara is neither inside the creation nor outside the creation but Ishwara is itself creation. Ishwara creates with the help of Maya. Maya has two powers.
- Aavaran Shakti
- Vikshepa Shakti
This is the covering power of Maya. By this power the beings in creation forget that they are 'Brahman'.Vivekachudamani verse 113 tells that Aavaran Shakti or Avritti Shakti is due to Tamas Guna of Maya.
This is the projecting power. By this power the universe which we see is projected in this way we see and observe.Vivekachudamani verse 111 tells that Vikshepa Shakti is due to Rajas part of Maya and it is projecting power.
Is Ishwara under influence of Maya ?
Ishwara himself is the wielder of Maya, Svetasvatara Upanishad 4.10 states:
मायां तु प्रकृतिं विद्यान्मायिनं च महेश्वरम्|
Maya is Prakriti and Maheswara (Ishwara) is the wielder of Maya.
Adi Shankara in Vivekachudamani says that Maya is Shakti of Ishwara ie. Paramesha Shakti:
अव्यक्तनाम्नी परमेशशक्तिरनाद्यविद्या त्रिगुणात्मिका परा।
कार्यानुमेया सुद्यियैव माया यया जगत्सर्वमिदं प्रसूयते।। 108
Maya or Avidya called undifferentiated (Avyakta) is the power of the Lord. It is without beginning is made of three Gunas and is superior to the effects. She is to be inferred by one of clear intellect only from the effects she produces. It is She who brings forth this whole universe.
Ishwara is Saguna and saguna form is taken by the help of Maya. But still the nature of Ishwara is defined as Sarvagya (ie. All knowing).
Example in Kena Upanishad Bhasya when Uma manifests among devas, in that section Adi Shankara has mention Saguna Ishwara (in that case case Shiva) as 'Sarvajna Ishwara'. Thus Ishwara has various qualities like Sarvajnata and hence he can't be deluded by Maya.
How Ishwara creates ?
Creation is the innate nature of Ishwara. As Taittariya Upanishad says
2.6.1 He (the Self) wished, “Let me be many, let me be born. He undertook a deliberation. Having deliberated, he created all this that exists. That (Brahman), having created (that), entered into that very thing. And having entered there, It became the formed and the formless, the defined and the undefined.."
So he wished and he became many. So he himself is the creation. So everything in this Vyavaharik level (including ourselves) which we see is simply Ishwara himself.
What is the origin of Maya?
Maya is generally called called as Anirvachaniye (inexplicible). In the above quote also we see Adi Shankara says Maya as "It is without beginning" and "to be inferred by Clear intellect only". One gets deluded by Maya due to Vaasanas (desires) which are accumulated in the mind. How desires originated ? Desires are originated because it is originating now. It is seen through 'Pratakshya Pramanam' ie. Direct Perception. We can't trace first origin of it. But it originated because it caused Maya and Maya caused Ishwara Shristi. And as we can see Ishwara Shristi right now here, thus it originated. As we can't trace first origin of vasaana and hence we can't also trace origin of Maya and it leads to infinite regression. And Hence Maya is called to be existing from beginning.
How we got individuality ?
In Paramarthika level there is no individuality as only Brahman in Satchidananda Swarup exists there. But in Vyavaharik level we see individuality. As Vyavaharik level is due to Maya of Ishwara. Hence it is responsible for our individuality. As Upanishads declare 'he became many...'. Thus at this time individuality arose due to Aavaran(covering) power of Maya. It is described as Akash GhatAkash Vaad. Here Aakash is infinite and Ghat akash means part inside infinite. Due to influence of Maya a small portion called Ghat-Akash is covered by Mind Intellect and other sheath to satisfy it's desire (called vaasanas). Individuality arises at this stage.
Standard analogy example:
The standard example given to represent creation in Advaita is dream world. We see dream due to unsatisfied desires remained as impressions in our mind which are called Vasanas. Due to Nidra Shakti (analogous to Maya Shakti) we see dream and due to Vikshepa(projecting power) we create a new dream world. Just as Ishwara creates this world by himself (multiplying). Due to Anavaran (covering) power of Nidra shakti (ie. Maya) we forget we are dreaming and as we ourselves are also in dream world and now we began to think world and us as separate. This process continues until we possesses sharp intellect with Jnanam. Thus creation by Ishwara is analogous to our creation of dream world.
Moksha in Advaita is not like other philosophies like Visishistadvaita, Dvaita and other where a Jeeva goes to Kailash/ Vaikuntha and enjoys with Lord there (though if one attains lokas like Brahmaloka and Vishnuloka through sadhana he doesn't return from there as his Jnana is guranteed there (Shankara Bhasya 3.3.31)). In Advaita everyone is already 'Nitya Jeevan Mukta' ie. Already Liberated itself. Only knowledge is required to know this. When he gets knowledge he gets liberated immediately instantaneously (in the same way darkness is instantaneously removed from candle.) This state is also mentioned in Dakshinamurty stotra of Adi Shankara as:
"प्रागस्वाप्समिति प्रबोधसमये यः प्रत्यभिज्ञायते,
" That state is experienced during Spiritual Awakening whereby one clearly Perceives that "Before I was Sleeping"
He may go on doing normal activity inside body to destroy Prarabdha karamas. But he is not affected by such Karmas as he knows he is not that body, mind and intellect but he is the Supreme Sat-Chidananda-Brahman.
What happens after death?
There is no meaning of death here. It is just casting of Sthula Sarira. As he don't possess desire he isn't attracted to have any new Sharira/body. So he don't have rebirth. He is in the highest blissfull state so he doesn't desire to do any other thing or to get reborn in Samsara or other.
Even the Gods can't prevent him from doing anything as he is the self of everything(ie. Even God's also) as Brihadaranyaka Upanishad says:
1.4.10 And to this day whoever in like manner knows It as, ‘I am Brahman’, becomes all this (universe). Even the gods cannot prevail against him, for he becomes their self.
But he rarely chooses to do anything as he is in the most blissful state. So anything he does is of lower bliss than that state. But he may also, as Suka in Mahabharat did so one time. He pronounces 'Bho' and entire universe pronounced 'Bho' as he had became self of all. He did it to calm grieving Veda Vyas.
Meanwhile, the righteous-souled Suka, who had entered the elements, had become their soul and acquired omnipresence, answered his sire by uttering the monosyllable Bho in the form of an echo. At this, the entire universe of mobile and immobile creatures, uttering the monosyllable Bho, echoed the answer of Suka. (Shanti Parva chapter 320)
Thus for other people after moksha also he gets individuality as moksha/liberation can happen while being in Sarira also. But for him there is no individuality as he donot identify himself as body, mind and intellect. After death also sheath of mind and intellect are there. But he may choose only to live in Paramarthika level by casting off mind and intellect thus we may here call it lost it's individuality. But there is no meaning of calling it losing individuality as individuality itself was illusion at the first time and creation itself took place by " he became many...".
Note: I had written this answer several years ago. Today, I have added
some more references to it. As I'm not initiated into the lineage
established by Adi Shankara (and as true knowledge is obtained through
Guru Parampara) it is possible that I might have misrepresented some of
the core principles of Shankara Advaita in this answer. If you feel
that something is being misrepresented please do comment about it or