Basics of Advaita philosophy:
1) Three levels of truth:
A) The transcendental or the Paramarthika level in which Brahman is the only reality and nothing else;
B) The pragmatic or the Vyavaharika level in which both Jiva (living creatures or individual souls) and Ishvara are true; here, the material world is completely true, and,
C) The apparent or the Prathibhasika level in which even material world reality is actually false, like illusion of a snake over a rope or a dream.
2) Brahman, the Nirguna Brahman:
According to Adi Shankara, God, the Supreme Cosmic Spirit or Brahman is the One, the whole and the only reality. Other than Brahman, everything else, including the universe, material objects and individuals, are false. Brahman is at best described as that infinite, omnipresent, omnipotent, incorporeal, impersonal, transcendent reality that is the divine ground of all Being. Brahman is also beyond the senses. It is the basis of the material world, which in turn is its illusionary transformation.
Due to ignorance (avidyā), the Brahman is visible as the material world and its objects. The actual Brahman is attributeless and formless. It is called as Nirguna Brahman. It is the Self-existent, the Absolute and the Imperishable. Brahman is actually indescribable. It is at best "Satchidananda" (merging "Sat" + "Chit" + "Ananda", ie, Infinite Truth, Infinite Consciousness and Infinite Bliss).
3) Maya:
According to Adi Shankara, Maya is the complex illusionary power of Brahman which causes the Brahman to be seen as the material world of separate forms. It has two main functions — one is to "hide" Brahman from ordinary human perception, and the other is to present the material world in its stead. Maya is also said to be indescribable, though it may be said that all sense data entering ones awareness via the five senses are Maya, since the fundamental reality underlying sensory perception is completely hidden. Maya is neither completely real nor completely unreal and hence indescribable. Its shelter is Brahman, but Brahman itself is untouched by the illusion of Maya, just like a magician is not tricked by his own magic.
Adi Shankara claims that the world is not absolutely unreal (false). It appears unreal (false) only when compared to Brahman. In the pragmatic state, the world is completely real—which occurs as long as we are under the influence of Maya. The world cannot be both true and false at the same time; hence Adi Shankara has classified the world as indescribable.
4) Ishvara, the Saguna Brahman:
According to Advaita Vedanta, when man tries to know the attributeless Brahman with his mind, under the influence of Maya, Brahman becomes the Lord. Ishvara is Brahman with Maya — the manifested form of Brahman. Adi Shankara uses a metaphor that when the "reflection" of the Cosmic Spirit falls upon the mirror of Maya, it appears as the Supreme Lord. The Supreme Lord is true only in the pragmatic level — his actual form in the transcendental level is the Cosmic Spirit.
Ishvara is Saguna Brahman or Brahman with innumerable auspicious qualities. He is all-perfect, omniscient, omnipresent, incorporeal, independent, Creator of the world, its ruler and also destroyer. He is causeless, eternal and unchangeable — and is yet the material and the instrumental cause of the world. He is the subject of worship. He is the basis of morality and giver of the fruits of one's Karma. However, He himself is beyond sin and merit. He rules the world with his Maya — His divine power.
This association with a "false" knowledge does not affect the perfection of Ishvara, in the same way as a magician is himself not tricked by his magic. However, while Ishvara is the Lord of Maya and she (ie, Maya) is always under his control, the living beings (jiva, in the sense of humans) are the servants of Maya (in the form of ignorance). This ignorance is the cause of the unhappiness and sin in the mortal world. While Ishvara is Infinite Bliss, humans are miserable. Ishvara always knows the unity of the Brahman substance, and the Maya nature of the world. Ishvara can also be visualized and worshipped in anthropomorphic form as deities such as Shiva, Vishnu or Devi.
5) Atman:
The soul or the self (Atman) is identical with Brahman. It is not a part of Brahman that ultimately dissolves into Brahman, but the whole Brahman itself. Atman is only one and unique. Indeed Atman alone is Ekaatma Vaadam. It is a false concept that there are several Atmans (Anekaatma Vaadam)Reality and Bliss are its characteristics. Atman, being the silent witness of all the modifications, is free and beyond sin and merit. It does not experience happiness or pain because it is beyond the triad of Experiencer, Experienced and Experiencing. It does not do any Karma because it is Aaptakaama. It is incorporeal and independent.
When the reflection of atman falls on Avidya (ignorance), atman becomes jiva — a living being with a body and senses. Each jiva feels as if he has his own, unique and distinct Atman, called jivatman. The concept of jiva is true only in the pragmatic level. In the transcendental level, only the one Atman, equal to Brahman, is true.
6) Salvation, Liberation or Moksha:
Advaitins also believe in the theory of reincarnation of souls (Atman) into plants, animals and humans according to their karma. They believe that suffering is due to Maya, and only knowledge (called Jnana) of Brahman can destroy Maya. When Maya is removed, there exists ultimately no difference between the Jiva-Atman and the Brahman. Such a state of bliss when achieved while living is called Jivan mukti.
While one is in the pragmatic level, one can worship God in any way and in any form, like Krishna or Siva as he wishes. Adi Shankara himself was a proponent of devotional worship or Bhakti. So Adi Shankara established the Shanmatha worship.
7) Theory of creation:
Every Astika darshana aims at establishing the correct relation between the triputi named jiva, jagat and Ishvara. Generally, this relationship is of the nature of karya and karana. Astika darshanas hold brahma to be the karana for jagat. karana can be of three types: upadana, nimitta and sadharana. Satkaryavada is an important aspect of samkhya theory. The word satkarya indicates the aspect of satta or asthitva of karya. Thus, it can be stated that satkaryavada is all about the abivyakti of karana as karya. This abivyakti is aided by the vyapara of the karana.
For example, if til seeds are seen as karana, til oil would be the karya. Even before the vyapara of extraction of oil from the seeds, the oil is already present in the seeds i.e. vyapara does not newly generate karya, but only helps in the abhivyakti of karya. When karana becomes vyaparashIla i.e. til seeds are accompanied by the vyapara of extraction, the karrana named til needs manifests as til oil, the karya. Due to this process of manifestation of karana as karya, the karana here is referred to as upadana. Thus, the samarthya of karana to manifest as karya is the key aspect to be noted here.
According to satkaryavada, karya is neither newly created nor destroyed and is ever present in the karana.
When karana is associated with vyapara, which we can call shakti, karya becomes evident.
One can consider the example of a tortoise stretching its limbs out of the shell and withdrawing them inside again. When there is abivyakti of karya from karana, it gets called as utpatti or creation and when there is tirodhana of karya in karana, it gets described as nasha or destruction.
Thus, neither utpatti nor nasha of the karya is true but these are rather vikaras or transformations. Also, they can be described as the vyaparas or activities of the karana.
Vivartavada and parinamavada can be described as two branches of satkaryavada. Vivarta can be interpreted to mean change, transform, turn around, appear altered or illusion. The relation between an actual object and its reflection within a mirror is one of vivarta. A jignasu describes vivarta as the false notion that is characterized by anyathabhava from tattva.
In advaita vedanta, vivarta is illustrated through two popular examples: sarparajju nyaya and shuktirajata nyaya. One can get the false impression of seeing a snake on seeing a rope or of seeing silver on seeing a shell. The adhyasa (misconception or erroneous attribution) named jagat occurs on Brahman on account of avidya (nescience).
Though the karana named Brahman, due to vivarta, appears as the karya named jagat, there is no separate karya in reality. Thus, only the karana or Brahman is satya and jagat is mithya. Though one is initially confused by the appearance of snake, he eventually realizes the true nature of that vastu as rajju. Similarly, true knowledge or brahmajnana is attained on adhyasa nirasana.
At the pragmatic level, the universe is believed to be the creation of the Supreme Lord Ishvara. Maya is the divine magic of Ishvara, with the help of which Ishvara creates the world.
The serial of Creation is taken from the Upanishads. First of all, the five subtle elements (ether, air, fire, water and earth) are created from Ishvara. Ether is created by Maya. From ether, air is born. From air, fire is born. From fire, water is born. From water, earth is born. From a proportional combination of all five subtle elements, the five gross elements are created, like the gross sky, the gross fire, etc. From these gross elements, the universe and life are created.