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There are three main ways of understanding creation in the advaita tradition - namely, ajAti vAda (creation is not an absolute, real event), sRshTi-dRshTi vAda (what has been created is perceived) and dRshTi-sRshTi vAda (perception is simultaneous with creation). The ajAti view is held in the pAramArthika sense, while the other two views are held in the vyAvahArika sense. As in most issues in advaita philosophy, the writings of Sankara themselves draw upon all these views, while later writers develop upon one or the other view. The ajAti vAda is mainly elaborated by gauDapAda, Sankara's paramaguru. However, please remember that the advaita tradition is one of oral teaching, and therefore the description that follows is not exhaustive. A given teacher may use one or more of these vAdas, depending upon his own views, the student's ability, and other factors.

sRshTi-dRshTi vAda :-
Whether of the bhAmatI or of the vivaraNa school of post-Sankaran advaita, most authors start off assuming the universe. For the beginning student, this makes sense, because everybody starts off by observing a universe distinct from "oneself", and believing that this observed universe has a distinct reality apart from "oneself". So long as this "oneself" is identified by the observer, not with the Atman, but with anAtman, advaitins would say that there is a difference between the observed ("the universe" which, by the way, is wrongly perceived) and the observer (the "oneself" which is wrongly identified). At this stage, there is still ignorance about the true nature of external things and oneself. Taking this ignorance into account, and referring to the IkshaNa-Sruti (tadaikshta bahusyAm prajAyeya - this sentence occurs almost every time there is talk of creation in the upanishads, as in the sad-vidyA section of the chAndogya), the universe is held to be created by brahman in His capacity as ISvara. This is the sRshTi-dRshTi vAda, i.e. the universe that is seen has been created by ISvara. sRshTi (creation) is therefore prior to dRshTi (perception). In other words, advaita vedAnta can accept the view that a thing has to exist, in order for it to be perceived. Note that this view also entails what is known as aneka-jIva vAda - the view that there are multiple jIvas, corresponding to numerous sentient individuals in the universe.

However, it is pointed out that to even talk of creation, one has to assume avidyA, and one has to admit of mAyA, as the power of ISvara. Under this view, mAyA is accorded a measure of reality with respect to the observed universe, and is similar in many respects to the notion of prakRti in sAm.khya. Still, it is denied that this mAyA has an independent existence or reality of its own. It is made absolutely dependent on brahman, which is the sole reality. It is this position that differentiates advaita vedAnta from the dualistic sAm.khya, although some authors of the bhAmatI school may write in such a way as to make this distinction very fuzzy indeed. Inasmuch as the only independent cause is brahman as ISvara, and so far as it is held that the mAyA disappears when brahman is truly known, this view is still non-dual in its teaching. This notion of brahman as ISvara, with attributes, who appears to be different from the creation, is therefore described as the "taTastha-lakshaNa" - a temporary description for the purposes of explaining creation to those who seek one. This temporary description does not mean that non-duality is compromised. The sRshTi-dRshTi view may help the layman to understand the fact that throughout the ages, advaitins have by and large been very devoutly religious people, who worship their chosen deity. They do not think that this affects non-duality in any way. So much for vyavahAra.

ajAti vAda :-
The notion that mAyA has no reality in itself, and that brahman is the only real, allows the sRshTi-dRshTi vAdin to "graduate", so to speak, to ajAtivAda, the view that no creation really occured ever. Although one initially starts looking for brahman as the ontological basis of the perceived universe, advaita also recognizes that this search for origins is ultimately futile, as far as moksha is concerned. It is pointed out that moksha means that the Atman is fully known as brahman Itself. Therefore, understand the Atman first, theories about how this creation came about can wait. Until now, the questioner has been concerned mainly with explaining the external world, which (s)he knows only through the operation of the senses. The identity propounded by the upanishads (between the Atman and brahman) opens up an even more fascinating inner world that is not seen by the eye, not heard by the ear and not felt by touch. It is this inner search that allows the sAdhaka to acquire the jnAna to deny mAyA any reality whatsover. At this stage, brahman, which was previously understood to be with attributes, is understood in its essence to be really nirguNa. This essential nature of brahman is described as "svarUpa-lakshaNa" - a description that captures the real nature of brahman. When brahman is apprehended as the nirguNa, without any attributes, mAyA completely disappears. The universe too, consequently has to disappear. This is the most difficult thing for anybody to understand and accept, because the senses constantly seem to remind one of the presence of the universe. But then, the unitary understanding of the Atman as identical to brahman occurs only at the turIya (the fourth) state, not in the jAgrat (waking), svapna (dream) and sushupti (deep sleep) states. As the mANDUkya upanishad reminds us, the turIya is adRshTam (unseeable), avyavahAryam (non-relational), agrAhyam (ungraspable), alakshaNam (without any attributes), acintyam (unthinkable), avyapadeSyam (cannot be indicated as an object), ekAtma-pratyaya-sAram (the essence of cognition of the One Atman), prapancopaSamam (that into which the entire universe is resolved), SAntam (peaceful), Sivam (auspicious), advaitam (non-dual).

As far as creation theories are concerned, the most important adjectives in the mANDUkya's list, in my opinion, are prapancopaSamam - that into which the world is resolved, and ekAtma-pratyaya-sAram - the essence of cognition of the One Atman. These words indicate that in the turIya state, the mistaken identification of the Atman with anAtman has ceased, and there is no more external world perceived as separate from oneself. The "oneself" that was previously talked about doesn't exist anymore, and the world external to this "oneself" also does not exist anymore. Only the One Atman remains. It is only at this stage that it makes sense to talk of ajAti. The word prapancopaSamam indicates that the world-in-itself has no existence. It is as if this world that was previously seen as external to "oneself", along with the "oneself" that was previously mistakenly identified with things other than the Atman, is now resolved into the One Atman, the one and only Reality.

The same idea is mentioned in the bRhadAraNyaka - yatra tvasya sarvam AtmaivAbhUt, tatra kena kam paSyet? etc. leading to vijnAtAram are kena vijAnIyAt? In the state of non-duality, the One Atman itself is the whole world; there is nothing other than this Atman, so talk of a world external to this Atman does not even arise. The questions posed by the bRhadAraNyaka indicate that there are no senses of sight, smell, touch etc. that can operate at this state. Hence the question, vijnAtAram are kena vijAnIyAt? - how is the knower to be known? i.e. not through the senses. The knower knows itself, immediately, and there is no distinction between the knower, the means of knowledge and the object of knowledge. I will restrict the urge to indulge in poetic fancy about the ineffable nature of this vijnAtA, and the experience that defies words. Reverting to our concern about creation, we can say this much. As the question of creation does not even arise when the identity of Atman with brahman is known, it follows that nothing either comes into being nor goes out of being - it is always self-existent. This is ajAtivAda. The Atman is eternal, unborn and undying, admitting of no divisions. As the creation (prapanca) has been resolved (upaSamam) into this One Atman Itself, prapanca can be described as not created. This is the paramArtha. Returning to vyavahAra, one comes back to the jAgrat, svapna and sushupti states, but the knowledge gained in the turIya state remains, and the preliminary sRshTi-dRshTi view loses much of its significance.

Thus, traditional advaita vedAntins generally handle creation by provisionally explaining it in terms of sRshTi-dRshTi vAda, followed by a subsequent ajAti vAda argument, which denies that creation is an event that took place at some given point of time in the past. This approach follows the adhyAropa-apavAda method (sublation of superimposition), and is closely tied to the vyavahAra and paramArtha ways of understanding reality. So far as the paramArtha is held to be the only Real, ajAti is upheld. sRshTi-dRshTi is accepted only in the vyAvahAric sense, and needs to be transcended along with the rest of vyavahAra, for the sake of moksha.

This description of creation theories in advaita holds true for those authors who want to approach the paramArtha through the vyavahAra, i.e. from sRshTi-dRshTi to ajAti. There are other authors like SrIharsha, citsukha and sukhaprakASa, who care not a whit for vyavahAra, and do not feel the need to even talk about creation. These authors are masters of dialectic, much like nAgArjuna, and are interested in demolishing the logical premises of any question or definition that presupposes duality. As an aside, these authors are quite aware that their method is very close to the madhyamaka approach, but they categorically assert brahman as the only absolute, and still find fault with nAgArjuna for not asserting the existence of one absolute.

dRshTi-sRshTi vAda :-
This brings me to the third view, namely dRshTi-sRshTi vAda - the view that cognition and creation are simultaneous. It is generally assumed that this view was first propounded by prakASAnanda sarasvatI (ca. 16th century CE) - in his vedAnta-siddhAnta-muktAvalI. This author also wrote texts on SrIvidyA, such as tArAbhakti-tarangiNI. It is generally assumed that this view is an entirely new position, unknown to earlier authors in the advaita tradition. However, it should be pointed out that the gauDapAdIya kArika also teaches a very similar view in its arguments leading up to ajAti vAda. This view comes close to many schools of subjective idealism and to the buddhist vijnAnavAda. It also seems to throw up the most interesting logical paradoxes that are familiar to those interested in interpretations of quantum mechanics, e.g. the act of observation itself causing a particular collapse of a wave function, thus creating its outcome in some sense, and the absolute necessity of the observer in any description of an event.

Within traditional vedAnta discourse, numerous objections can be raised against this view. If ISvara exists in the vyAvahAric sense, then is he the creator of the universe or not? If yes, dRshTi-sRshTi vAda is contradicted, for it holds that the jIva creates simultaneously with cognition. This means there are multiple creators, in addition to ISvara. If it is said that the jIva and ISvara are both brahman and the created entity is also brahman (since everything is brahman), so that the creation by a jIva does not contradict ISvara's creatorship, the objection to this would be that such a view ends up partitioning brahman into several different real entities, but brahman cannot be so divided. If ISvara is said not to be the creator, then this view contradicts Sruti. Besides, what is the practical use, to the spiritual aspirant, of admitting such an ISvara?

In answer to all these objections, it should be emphasized that the dRshTi-sRshTi view is also closely allied to what is known as the eka-jIva vAda, and cannot be viewed independently of it. The eka-jIva vAda holds that, ultimately speaking, there is only one jIva, which is identical with brahman. If this is understood, all the above objections simply vanish. There is no question of multiple creators, as there is only the one jIva, identical with brahman. The dRshTi-sRshTi vAdin also does not "really" partition brahman into several different entities. On the contrary, it is the above mentioned objector who actually assumes that brahman can be so partitioned. As for the practical use to the spiritual aspirant, the dRshTi-sRshTi view is freely admitted to be useful only for the advanced sAdhaka who does not cling to a view of multiple, real jIvas. Such an aspirant also does not define his ISvara with respect to the creation, and is, in fact, better suited to really understand what the Sruti means, when it says that brahman creates by mere seeing (tad aikshata).

I would like to end on a note of caution against reading too much into the names of these vAdas. The names are meant to capture the most significant thread of discussion in each vAda, but it is easy to be misled into an analysis of the respective positions that concentrates only on their names and forgets all the other allied arguments that are not specifically mentioned in the name. Each vAda touches upon every issue that is of concern to the advaita vedAntin, but in slightly different ways. Besides, a given advaita teacher may teach different aspirants differently, based on differing aptitudes. All vedAntins of non-advaita schools are necessarily sRshTi-dRshTi vAdins in their own way, but they can never be dRshTi-sRshTi vAdins or ajAti vAdins. An advaitin, on the other hand, may teach students according to either dRshTi-sRshTi vAda or sRshTi-dRshTi vAda, but all versions of these vAdas will return to the basic Atman = brahman equation. In the final analysis, as long as moksha remains the prime issue around which every discussion revolves, ajAti vAda always remains, and every advaitin returns to it, whatever other vAda he uses when talking of vyavahAra. Thus, no true advaitin will deny ajAtivAda, although he may rarely talk of it, and he probably will not actively teach it to anybody but the most advanced student.