that which pervades all this is indestructible
अविनाशि तु तद्विद्धि
येन सर्वमिदं ततम्
Know that alone to be imperishable, which pervades this universe; for no one has power to destroy this indestructible substance.
Concepts
आत्मा
ātman
Of debated Vedic root (possibly √an, 'to breathe') — the self, breath, or essence understood to sit beneath and prior to body and mind.
Arjuna's grief in chapter one is grief for bodies — people he loves, about to die. Chapter two's whole opening move is Krishna redirecting that grief toward a question modern readers ask just as urgently: is there anything in a person that death doesn't reach?
that which pervades all this is indestructible
अविनाशि तु तद्विद्धि
येन सर्वमिदं ततम्
Know that alone to be imperishable, which pervades this universe; for no one has power to destroy this indestructible substance.
never born, never dies, unchanging
न जायते म्रियते वा कदाचि
न्नायं भूत्वा
भविता वा न भूयः
The soul is never born nor dies; nor does it become only after being born. For it is unborn eternal, everlasting and ancient; even though j the body is slain, the soul…
casts off worn bodies like old clothes
वासांसि जीर्णानि यथा विहाय
नवानि गृह्णाति नरोऽपराणि
As a man shedding worn-out garments takes other new ones, likewise the embodied soul, casting off worn-out bodies, enters into others which are new
unburnable, unwettable, unmoving, eternal
नैनं छिन्दन्ति शस्त्राणि
नैनं दहति पावकः
Weapons cannot cut it, nor can fire burn 0 it;,. water cannot wet it nor can wind dry
The self the Gītā means is the one thing about you that was never born — so it cannot die (2.20). Body, mind, memory: all of it changes and ends. The knower of all that doesn't. Śaṅkara says that knower is finally Brahman itself; Rāmānuja says it is an eternal soul held by the Lord — a real disagreement, and an old one. But the verse's comfort doesn't wait for it to be settled: what you actually are is not what dies.

Ādi Śaṅkarācārya · Advaita
For Śaṅkara the verse denies the self any of the six changes bodies undergo — not merely long-lived, but of a different order than the body entirely.
The Self has no change in the form of being born… It is birthless, and since It does not die, therefore It is eternal.
Sastri tr. (1897), on 2.20

Śrī Rāmānuja · Viśiṣṭādvaita
Rāmānuja affirms the same indestructibility but keeps the self a real, individual knower dependent on Īśvara, not identical with an undifferentiated absolute.
All the attributes of the insentient [body], like birth, death, etc., never touch the self.
Gītā-bhāṣya, on 2.20 (translation attribution under review)
Where the traditions differ, we show the difference.
The Bhagavad Gītā
He who regardeth this as a slayer, and he who thinketh he is slain, both of them are ignorant. He slayeth not, nor is he slain.
The soul is never born nor dies; nor does it become only after being born. For it is unborn eternal, everlasting and ancient; even though j the body is slain, the soul is not. (20)
The Upaniṣad
The knowing Self is not born, it dies not; it sprang from nothing, nothing sprang from it. Unborn, eternal, everlasting, this ancient one is not killed, though the body is killed… If the slayer thinks that he slays, if the slain thinks that he is slain, both of them do not understand: he neither slays nor is he slain.
Kaṭha Upaniṣad I.2.18–19, tr. F. Max Müller, Sacred Books of the East vol. 15 (1884)
The Gītā is widely read as directly absorbing these Upaniṣadic verses.