The doctrine of the Atman — the imperishable Self that survives every birth and every death — is the metaphysical foundation on which the entire Gita rests. Krishna's first substantive teaching in Chapter 2 is not about action, or devotion, or meditation, but about identity. Arjuna is grieving for kinsmen he thinks he is about to kill; Krishna's response is that no one truly kills and no one is truly killed, because the essential person is not the body at all.
The verses that follow — 2.11 through 2.30 — form the Gita's most concentrated statement of Vedantic anthropology. The Self is unborn, eternal, ancient. Weapons cannot cut it, fire cannot burn it, water cannot wet it, wind cannot dry it (2.23-24). It is the wearer, not the garment; the seer, not the seen. Its recognition is the end of grief.
But the teaching is not offered as consolation. Krishna gives it to Arjuna as a call to action. Because the Self cannot be destroyed, action can be undertaken with equanimity; because the body is a garment, its wear and loss are not tragedies. The knowledge of the Atman is what makes Karma Yoga possible: only one who knows he cannot die can act without craving to survive.
Chapters 13 and 15 return to the theme with philosophical precision — Chapter 13 distinguishes the field (the body-mind complex) from the knower of the field (the Self); Chapter 15 describes the Self as an eternal fragment of the Divine, seated in the heart of every being. Read together, these verses form a complete Vedantic catechism.