Vakya Vritti is a Vedantic textbook

Textbook

A textbook or coursebook is a manual of instruction in any branch of study. Textbooks are produced according to the demands of educational institutions...

 that concerns itself with the detailed and elaborate explanation of one of the Mahāvākyas

Mahavakyas

The Mahavakyas are "The Great Sayings" of the Upanishads, the foundational texts of Vedanta. Though there are many Mahavakyas, four of them, one from each of the four Vedas, are often mentioned as "the Mahavakyas"...

 "Tat Tvam Asi

Tat Tvam Asi

Tat Tvam Asi , a Sanskrit sentence, translated variously as "That thou are," "Thou are that," "You are that," or "That you are," is one of the Mahāvākyas in Vedantic Sanatana Dharma...

". It was compiled by Adi Shankara

Adi Shankara

Adi Shankara Adi Shankara Adi Shankara (IAST: pronounced , (Sanskrit: , ) (788 CE - 820 CE), also known as ' and ' was an Indian philosopher from Kalady of present day Kerala who consolidated the doctrine of advaita vedānta...

charya and is in the form of a dialogue between a student and a great rishi

Rishi

Rishi denotes the composers of Vedic hymns. However, according to post-Vedic tradition, the rishi is a "seer" to whom the Vedas were "originally revealed" through states of higher consciousness. The rishis were prominent when Vedic Hinduism took shape, as far back as some three thousand years...

(enlightened seer)

The Major Premises

The dialogue of the Vakya Vritti can be thought of as having the following major premises:

1) Tvam (You) refers to the spark of Divinity

Divinity

Divinity and divine are broadly applied but loosely defined terms, used variously within different faiths and belief systems — and even by different individuals within a given faith — to refer to some transcendent or transcendental power or deity, or its attributes or manifestations in...

 within each sentient being, which enlivens that being

2) Tat (That) refers to the immortal Brahman

Brahman

In Hinduism, Brahman is the one supreme, universal Spirit that is the origin and support of the phenomenal universe. Brahman is sometimes referred to as the Absolute or Godhead which is the Divine Ground of all being...

, the source of all life all around

3) Asi (are) refers to the Tvam-substance and the Tat-substance as being the same entity