Bhagavad Gita on reincarnation

Just as in the physical body of the embodied being is the process of childhood, youth, old age; similarly in the transmigration from one body to another the wise are never deluded.

But know that by whom the entire physical body is pervaded is indestructible. No one is able to cause the destruction of the imperishable soul.

The soul never takes birth and never dies at any time nor does it come into being again when the body is created. The soul is birthless, eternal, imperishable and timeless and is never terminated when the body is terminated.

As a person gives up old and worn out garments and accepts new apparel, similarly the embodied soul giving up old and worn out bodies verily accepts new bodies.

The soul is indestructible, the soul is incombustible, insoluble and unwitherable. The soul is eternal, all pervasive, unmodifiable, immovable and primordial.

For one who has taken birth, death is certain and for one who has died, birth is certain. Therefore in an inevitable situation understanding should prevail.