Where is this 'Self'?

  There are the Adhyatma Upanishad, Koushitaki Upanishad and many others which give details about the Atman, the Self of All. The Bhagavad-Gita defines what is the Atman and the supreme Lord says, "He is the Self of All". 
 But where is this 'Self'? It is both within and outside the jiva, living beings! It has no specific place. The air we breathe divides itself into five prominent channels or divisions and spreads through out the body. There are also five sub-divisions besides the main. These support the body as the vital airs, the pranic energy. It (the air) is outside as well as inside! Is it the Self? No, it only serves the body as source of support! But, then what is the Self? This question can never be answered! If it is something other than the self, one can say this is this. If what we call the self is the only thing that exists and all else is its manifest forms how can one separate and say this is this? This is the enigmatic subject that attracts all intellectuals and the debate never ends! 
  What the Upanishad says about the 'Self' is very interesting. What cannot be explained, what implicit,or what cannot be expresses in words are expresses in innumerable ways, but still remains unexplained!  Several great sages have tried to explain  according to their understanding of the Self and some of these are quoted here in  the following. 

   "Those of his fellows who belong to him here and those who are dead and whatever else there is which he wishes for and does not obtain-he finds all that by going in there (i.e. into his own Self). For there, indeed, lie those true desires of his, covered by what is false. As people who do not know the spot where a treasure of gold has been hidden somewhere in the earth, walk over it again and again without finding it, so all these creatures day after day go into the World of Brahman and yet do not find it, because they are carried away by untruth. That Self abides in the heart. The etymological explanation of heart is this: This one (ayam) is in the heart (hridi); therefore It is called the heart (hridayam). He who knows this goes every day in deep sleep to Heaven (i.e. Brahman, dwelling in the heart). Now, this serene being, after rising from this physical body and attaining the Highest Light, reaches his own true form. This is the Self. Thus he (i.e. the teacher, questioned by his pupils) spoke. Continuing, he said: This is the immortal, the fearless. This is Brahman. And of this Brahman the name is Satyam, the True. This name Satyam consists of three syllables: Sat, ti and yam. That which is Sat signifies the Immortal; and that which is ti is the mortal; and yam binds them both. Because this syllable binds both, therefore it is called yam. He who knows this goes every day in deep sleep to Heaven (i.e. Brahman, dwelling in the heart)". [Sama Veda, Chandogya Upanishad VIII, III - The Serene Self and Satya Brahman, 2-5]

    "The self is a dam, a separating boundary, for keeping these worlds apart. This dam is not passed by day and night, by old age, death and grief, or by good and evil deeds. All evils turn back from It, for the World of Brahman is free from all evil." [Sama Veda, Chandogya Upanishad, VIII, IV - Brahman as a Dam, 1].

Then Maitreyi said: Just here you have completely bewildered me, venerable Sir. Indeed, I do not at all understand this. He replied: Certainly I am not saying anything bewildering, my dear. Verily, this Self is immutable and indestructible. This Self is That which has been described as 'Not this, not this.' It is imperceptible, for It is never perceived; undecaying, for It never decays; unattached, for It never attaches Itself; unfettered, for It never feels pain and never suffers injury.Through what, O Maitreyi, should one know the Knower? Thus you have the instruction given to you. This much, indeed, is the means to Immortality. Having said this, Yajnavalkya renounced home. [Yajur Veda, Brihadaranyaka Upanishad IV, V-Yajnavalkya and Maitreyi (II), 14-15]

   These words of the Upanishads are terse and difficult to understand. These doctrines are to be explained by a learned teacher.