The Māṇḍūkya Upaniṣad opens with one of the most extreme philosophical statements in the tradition: "Oṃ — this syllable is all this. Whatever was, is, or will be — all is indeed Oṃ. And whatever is beyond the three times — that too is Oṃ." In 12 verses it develops a complete philosophy of consciousness centred on the analysis of Oṃ into four elements corresponding to four states of human experience.
The four states — corresponding to AUM + silence
MāṇḍU 7 gives the most direct description of Turīya: it is not experientially inward-focused (as in dream), not experientially outward-focused (as in waking), not experientially blank (as in deep sleep). It is the consciousness that knows all three — the witnessing awareness that is never absent in any of the three states, but is never identified with any content of those states. It is advaita — not-two — pure, peaceful, auspicious. It is the Ātman — which should be known.
Gauḍapādakārikā — the commentary that shaped Advaita
The Māṇḍūkya's 12 verses would be significant on their own — but their philosophical importance is amplified enormously by Gauḍapāda's verse commentary (the Māṇḍūkyakārikā, also called Gauḍapādakārikā, c.6th–7th century CE), which extends the text to 215 verses across four books. Gauḍapāda is Govindapāda's teacher and Śaṅkara's grand-teacher — making the Māṇḍūkyakārikā the text through which the Advaita tradition was most directly transmitted to Śaṅkara.
Gauḍapāda's central contribution: the doctrine of ajātivāda (non-origination). Nothing has ever come into being; nothing will ever be destroyed. The appearances of creation, causality, multiplicity, and change are like the appearances in a dream: they arise, they seem real in the moment of arising, and they are discovered on waking to have had no independent existence. The Ātman (Turīya) has never been born, never been bound, and never needs to be liberated — it was never in bondage. This is the most radical statement of the Advaita position before Śaṅkara. Source: Gambhirananda (trans.), Māṇḍūkya Upaniṣad with Gauḍapādakārikā (Advaita Ashrama, 2000).
The dream analogy — the world as dream
Gauḍapāda's Kārikā 1.6–16 develops the dream analogy: dream objects are not real (they disappear on waking), but they seemed real while the dream lasted. Similarly, waking objects — which appear as external, independent, substantial — may have the same epistemic status as dream objects: they appear real in the context of ordinary waking experience, but from the standpoint of Turīya (enlightened awareness), their independence and substantiality may be equally a projection of consciousness. This is not quite the same as saying "the world is a dream" — Gauḍapāda is making a careful epistemological point, not a dismissive one. Source: Gambhirananda (2000), Kārikā 1.6–16.
MāṇḍU 1–12 (Olivelle, 1996). Gauḍapādakārikā (Gambhirananda, Advaita Ashrama, 2000).
Why the Māṇḍūkya is sufficient — Muktikā Upaniṣad
The Muktikā Upaniṣad (a minor, later Upaniṣad) contains a statement — attributed to Rāma — that the Māṇḍūkya Upaniṣad alone is sufficient for liberation: māṇḍūkyam eva alaṃ muktaye. Whether or not one accepts the Muktikā's authority, the claim reflects the tradition's assessment of the Māṇḍūkya's philosophical compression: in 12 verses it presents the complete Advaita teaching — the nature of Oṃ, the nature of consciousness, the four states, and the recognition of Turīya as the Ātman that is Brahman. The text is complete in a way that none of the longer Upaniṣads are: it does not illustrate or approach the recognition through narratives and dialogues but presents the recognition directly in the most concentrated possible form.
Śaṅkara's commentary on both the Māṇḍūkya and Gauḍapāda's Kārikā is the technical foundation of Advaita Vedānta's philosophical vocabulary — terms like vivartavāda (the doctrine of appearance), adhyāsa (superimposition), and adhiṣṭhāna (substratum) are developed in these commentaries and carry the entire architecture of the Advaita analysis of bondage and liberation. Source: Gambhirananda (2000).