Brahman and Atman

Some Upanishadic statements identify the Atman, the inner essence of the human being, with Brahman. While Advaita philosophy considers Brahman to be without form, qualities, or attributes, Visishtadvaita and Dvaita philosophies understand Brahman as one with infinite auspicious qualities. In Advaita, the ultimate reality is expressed as Nirguna Brahman. Nirguna means formless, attributeless, mega-soul, or spirit-only. Advaita considers all personal forms of God including Vishnu and Shiva as different aspects of God in personal form, Saguna Brahman i.e. God with attributes. In Visishtadvaita and Dvaita, God is Saguna Brahman with infinite attributes and is the source of the impersonal Nirguna Brahman, and God's energy is regarded as Devi, the Divine Mother.

The phrase that is seen to be the only possible (and still thoroughly inadequate) description of Brahman that humans, with limited minds and being, can entertain is the Sanskrit wordSacchidānanda, which is combined from sat-chit-ānanda, meaning "Being - Consciousness - Bliss".

The description of Brahman from Mandukya Upanishad:

सर्वं ह्येतद् ब्रह्मायमात्मा ब्रह्म सोयमात्मा चतुष्पात्
sarvam hyetad brahmāyamātmā brahma soyamātmā chatushpāt - Mandukya Upanishad, verse-2

• Translation:-

sarvam (सर्वम्)- whole/all/everything; hi (हि)- really/surely/indeed; etad (एतद्)- this here/this; brahma (ब्रह्म)- Brahma/Brahman; ayam (अयम्)- this/here; ātmā(आत्मा)- atma/atman; sah(सः)- he; ayam (अयम्)- this/here; chatus(चतुस्)- four/quadruple; pāt(पात्)- step/foot/quarter

• With the sandhi expanded:-

सर्वम् हि एतद् ब्रह्म अयम् आत्मा ब्रह्म सः अयम् आत्मा चतुस पात्
sarvam hi etad brahma ayam ātmā brahm sah ayam ātmā chatus paat

• Simple meaning:-

All indeed is this Brahman; He is Atman; He has four steps/quarters.

Vishnu is derived from the root "Vish" which means to enter or pervade, and He is called Vishnu because He pervades the whole universe. Brahmanda Purana (1.4.25) says that He is called as Vishnu because He has entered into everything in the universe. The most important aspect is that the whole universe is covered by only three steps of Vishnu which is referred to several times in the Vedas (Rig Veda 1.22.17, 1.154. 3, 1.155.4, Atharva Veda 7.26.5, Yajur Veda 2.25). In His three steps rests the whole universe (Rig Veda 1.154.2, Yajur Veda 23.49). All indeed is Brahman, which can thus be identified with Vishnu, based on the Vedas.