Brahman (ब्रह्मन्, neuter; not to be confused with the deity Brahma or the varna brahmana) is the central term of Upanishadic metaphysics. From the root √bṛh, "to grow, to expand", names that infinite reality from which the universe arises, in which it abides, and into which it dissolves.
Defining the Indefinable
The Taittiriya Upanishad 3.1 offers a working definition: yato vā imāni bhūtāni jāyante, yena jātāni jīvanti, yat prayanty-abhisaṁviśanti, tad vijijñāsasva, tad brahma — "that from which these beings are born, by which born they live, and into which they return — seek to know that; that is brahman". Elsewhere is called satyam jnanam anantam — truth, knowledge, infinite.
and
The tradition distinguishes saguna brahman (with qualities) and nirguna brahman (without qualities). is approached as Ishvara — personal, knowable, loved, worshipped. is as it is in itself — beyond name, form, and conception. The two are not different brahmans but two modes of human approach to one reality.
is described as sat-chit-ananda (सच्चिदानन्द): being, consciousness, and bliss. These are not three properties of a substance but three lights of a single infinite, articulated to assist meditation. To know is not to add a new piece of information; it is to recognise the one reality that has been there all along.
The Mahavakyas
Four "great sayings" (mahavakyas) from the Upanishads anchor the teaching. Prajnanam brahma (Aitareya 3.3) — consciousness is . Aham brahmasmi (Brihadaranyaka 1.4.10) — I am . Tat tvam asi (Chandogya 6.8.7) — that thou art. Ayam atma brahma (Mandukya 2) — this self is . Together they assert the identity, or at least the deep relation, of atma and .
Schools and Interpretations
The Vedantic schools differ on how to read these sayings. Advaita reads them as pure identity: there is only , and the apparent multiplicity is maya. Vishishtadvaita reads them as inseparable inherence: souls and world are the body of . Dvaita reads them as ontologically distinct: the self is dependent on, but never identical with, the Lord.
Practical Significance
Whatever the school, the practical orientation is shared. is not a remote object to be searched for but the very fabric of one's own awareness and of every appearing thing. The disciplines of study (shravana), reflection (manana), and meditation (nididhyasana) train one to live aware of this ground — and to find in that awareness the deepest peace.