Atma Described in Brahadharanyaka Upanishad.

Hare Krishna,Namaskarams.

Swami Paramarthananda teaches in his inimitable style this Upanishad which contains all the Upanishads in it. The chapter deals with brahmavidyA in I, 2, 3, 4 and 5^th sections. In fact Atma is best described in Brahadharanyaka Upanishad. The third section is called Jyotir brAhmaNam and the whole chapter is in the form of a dialogue between King JanakA and Rishi Yagnyalkya. I just try to give a glimpse of the teaching from my notes. I have also added some of the commentary portions in it. Any mistake in the following is due to my own limitation and should not be ascribed to Swamiji's teachings.
6^th Mantra: when Janaka asks the Rishi what exactly serves as light for man when the sun and moon has set, the fire has gone out and speech has stopped. Yagnavalkya answers, The self serves as his light. It is through the light of the self that he sits, goes out, works and returns in svapnA. This refers to the dream state where the the Atma the witness consciousness is available as the antara jyothi. In fact the svapna state is the ideal state to know the svayam jyothi Atma. Both this and the external light are used in the waking state.
7^th Mantra: Which is the self ? asks JanankA and the says: This infinite entity purushha that is identified with the intellect and in the midst of organs is the self effulgent light within the heart. Assuming the likeness of the intellect, it moves between the two worlds, it thinks, as it ware, and shakes, as it ware, .being identified with dream, it transcends this world- the forms of death (ignorance etc,).
Essence of this mantra is that I am not the body mind complex and just use it for transaction in the world. I am neither the karta nor pramAta. This jyotishhAm jyoth is the light of all lights in whose presence everything is known. This luminous self being finer than even the heart or intellect, unify, and impart its luster to the body and organs, including the intellect; etc; although within the intellect; for these have varying degrees of fineness or grossness in certain order, it being the innermost of them all.
9^th mantra: The essence of this mantra is that Atma is self effulgent at all times but clearly recognizable in dream. when one dreams he takes away a little of the impressions of the waking state and leaving the body aside creates for himself a dream body revealing his own light and dreams in this state. He himself becomes the light.
10^th mantra: The essence of this mantra is that mind is not self effulgent as it is matter and a changing vastu. Hence it becomes the object for the Atma the witness “I”. In this the jada part is mind, the effulgent part is Atma. Since the jIva leaves the body to go to dream state Atma is different from the BMI. By the illustration of dream it is proved that there is the self luminous Atman and that it transcends the forms of death, since it alternately moves between this world and the next. It is distinct from the nests of waking and dream states, therefore it is eternal. In sushhupti one gets the highest serenity and that state is called samprasadA.
23^rd Mantra: Essence if this mantra is that sushhupta svarUpam is Atma svarUpam. the nearest example of moksha. Atma has two visions 1) as citrupena has nirvikAra drishhti that is pure awareness. 2) As citAbhAsa rupena savikAra drishhti. While the first illumines the mind the other illumines the world, both functioning in jAgrat avasta. In short paramAtmarUpena pasyannapi jIvAtma rUpena pasyati.

With Krishna's blessings.