The Atman is our real self. The Atman is beyond death. By realizing this one transcends death. There is no other way to transcend death. You realize that immortal reality is my reality, then you transcend death. There was never a time when you were not there and there will never be a time when you will not exist ~ Krishna. The Atman is eternal. The Atman is devoid of absence before the birth and devoid of absence after death. There is the gross body, sthoola sharire, the subtle body, sookshma sharire and the causal body, Karana sharire, the Atman is beyond all 3. At death, the gross body dies but the subtle body continues. There is a dogma in science that the mind and consciousness are produced by the body and brain and that after death the person is also dead. This is called materialist reduction-ism and there is no proof for that. The gross body and subtle body are connected, but what happens after that is unknown to science. The sookshma and Karana sharire transmigrate(go from one body to another). This is bad news as then we are stuck in the cycle of rebirth, the limited existence continuously subject to suffering.
An intrinsic property is something that belongs to that entity and intrinsic property last as long as the entity exists. The fire has the power of burning. Milk is white. An accidental property is something that is gained and lost, borrowed. If a property is gained or lost, we know that it is accidental. If a property is not lost, then we know it's permanent or intrinsic. If you treat existence as a property (philosophically, existence is not a property), if there is an entity which has existence as an accidental property, then it will be born and destroyed. If an entity has existence as an intrinsic property then it always is, it is eternal. Since Atman is eternal, existence is an intrinsic property of Atman and this is called Sat (Pure Being). Therefore, you, the Atman, never stop existing and that which is not you never comes into existence. Atma Satyam Jagat Mithya. But how can we experience something which does not exist, it actually borrows existence from you. It appears to have an existence, this is an illusion. What is real is I am awareness, I am pure being and the whatever I experience in awareness, whatever I see to be an object of awareness is nothing really apart from me the pure being, it appears in me as if I experience it as it's another but its nothing other than me. Those who realize this have realized the truth.
So Atman is eternal and the only thing that exists, rest everything is non-existing borrowing existence from you. So either you are all of it or none of it, both lead to realization. Bondage is when you think I am only this (body) and everything else is separate from me.
This indestructible absolute eternal reality is all-pervasive. When your dreaming, all the people the very time and space were pervaded by me the dreamer. The same is true for consciousness and it's objects. Awareness does not change, all changes are noted in awareness. Now, this indestructible awareness is Atam which has existence as an intrinsic property. Then everything apart from you borrows existence from you just like everything in your dream borrows existence from you. You are Sat-Chit, pure awareness pervading everything that you experience. A question can come up, I am here and not there then how can I be all-pervading. The answer to that isn't here and there also in your awareness. If a person in your dream came up to you and said you are everything here, you wouldn't agree. But after getting up you would realize they were right. Atman is all-pervading. Then one might ask, where is it, where is your precious Atman. The answer to this question, Krishna says it's not an object to the instruments of knowledge. We deploy instruments of knowledge(senses) to know the world. But the Atman is not an object to these instruments, the senses cannot objectify Atman. The mind is used to conceptualising but the Atman is not an object of the mind too. Beyond mind beyond senses. But then to say something exist it must become an object of knowledge otherwise you can imagine anything(like happy potter exists). Atman is not the object of the senses or the mind rather it is the subject, it lights ups all the instruments to enable the use of them. If there was the photo taken, then there must be a photographer and though you can't see him/her, you know of their existence. Similarly, to use the 5 senses, to use the mind, even to doubt there is consciousness, you have to be conscious. Who is the one doubting, what is the one doubting? If you say everything is a dream, then there must be one thing that is not a dream, that is the dreamer. To experience these there must be an experiencer.
Atman is Akarta Abhogta. Without the body and mind, consciousness is neither a doer nor an experiencer. But with body and mind, you cannot but act. Do what is to be done. Then you're free of the bondage of karma. Atman is eternal, I am the reality of this universe everything apart from me is an appearance, this Atman pervades the entire world of appearance, it is not an object of the knowledge, you are neither the doer nor the experiencer, you, the Atman, are free of karma, you have to recognize that.