A mahāvākya - literally "great saying" (mahā + vākya) - is an Upaniṣadic declaration whose meaning, correctly understood, IS the liberating knowledge. Tradition names four canonical mahāvākyas, one from each of the four Vedas. Each declares the identity of the individual (jīva) with the absolute (Brahman) from a different angle. They are not devotional statements or metaphors - they are stated as fact, to be tested by direct inquiry.

One insight, four framings.

Each of the four is drawn from a specific Veda and its major Upaniṣad. Traditionally they are learned in this order - descriptive, declarative, instructive, experiential.

प्रज्ञानं ब्रह्म · prajñānaṃ brahma

"Consciousness is Brahman." The descriptive saying - points at what Brahman is. Not a definition (Brahman cannot be defined) but a pointer at the only thing already indubitable: the awareness reading this line right now. That awareness, not qualified by any object, is Brahman.

अहं ब्रह्मास्मि · ahaṃ brahmāsmi

"I am Brahman." The declarative saying, in the first person - the sage's realization spoken. Not the ego claiming divinity; the sense of "I" recognized as identical with the ground of everything. The Bṛhadāraṇyaka places it in the mouth of the primal Person on realizing his own nature.

तत्त्वमसि · tat tvam asi

"That thou art." The instructive saying - the teacher's pointer to the student. Uddālaka, teaching his son Śvetaketu, returns to this refrain nine times across chapter 6. "You are what you have been seeking as that." The oldest and most quoted of the four.

अयमात्मा ब्रह्म · ayam ātmā brahma

"This Self is Brahman." The experiential saying - the recognition itself, wordlessly. Points at the immediate Self (ayam ātmā, "this very Self, here") as none other than Brahman. The Māṇḍūkya's twelve verses are the shortest Upaniṣad and the one Gauḍapāda took as the basis for his Māṇḍūkya Kārikā, arguably the earliest systematic Advaita text.

The wider family of great sayings.

Beyond the four canonical mahāvākyas, the Upaniṣadic literature offers many other lines that traditionally serve the same pointing function. A sampling - most-cited first.

सर्वं खल्विदं ब्रह्म · sarvaṃ khalv idaṃ brahma

"All this, verily, is Brahman." The whole world of appearance, not exempt from Brahman. The universe seen through Advaitic eyes: not a rival to Brahman but Brahman's self-expression under name and form (nāma-rūpa).

नेति नेति · neti neti

"Not this, not this." The via negativa of the Vedas - the method of successive dis-identification. Every object of awareness (body, breath, mind, ego, even the sense of being an individual) is pointed at and set aside: not this either. What remains after every "not this" is what one always was.

एकमेवाद्वितीयम् · ekam evādvitīyam

"One only, without a second." The opening of Uddālaka's teaching in chapter 6 - the very same chapter that culminates in tat tvam asi. Non-duality stated in three Sanskrit words.

सत्यं ज्ञानमनन्तं ब्रह्म · satyaṃ jñānam anantaṃ brahma

"Brahman is truth, knowledge, infinity." Three attributes to point at what has no attributes - Śaṅkara reads them as lakṣaṇas (indicators) rather than viśeṣaṇas (qualifiers). satya eliminates falsity, jñāna eliminates unconsciousness, ananta eliminates limitation. What remains is the referent.

पूर्णमदः पूर्णमिदम् · pūrṇam adaḥ pūrṇam idam

pūrṇam adaḥ pūrṇam idaṃ pūrṇāt pūrṇam udacyate;

pūrṇasya pūrṇam ādāya pūrṇam evāvaśiṣyate.

"That is Whole; this is Whole; from the Whole, the Whole emerges. Take the Whole from the Whole - the Whole alone remains." The invocation prefixed to the Īśā Upaniṣad and used at the opening of the Bṛhadāraṇyaka. A mathematics of the infinite that does not obey subtraction.

नाहं मन्ये सुवेदेति नो न वेदेति वेद च

nāhaṃ manye suvedeti no na vedeti veda ca.

"I do not think I know it well, nor do I think I do not know it - I know, and I know not." The paradox at the limit of the pramāṇas - Brahman is neither an object of knowledge (thereby knowable) nor absent from knowing (thereby unknowable). The teacher who claims not to know is closer than the teacher who claims to know.

एकोऽहं बहु स्याम् · eko 'haṃ bahu syām

"I am one; may I become many." Brahman's own resolve - the source-declaration of manifestation itself. Cited across the tradition as the reason there is anything rather than nothing.

सोऽहम् / हंस · so'ham / haṃsa

"I am He." Read in reverse: haṃsa - the swan, ancient symbol of the liberated ātman. Used as a natural mantra keyed to the breath: so on the in-breath, haṃ on the out-breath. The mantra one does not have to remember to say - the body is already saying it.