The Chhandogya Upanishad is one of the most prominent among the major group of philosophical and mystical sanskrit texts of ancient India. This passage talks about the meaning of the real Self.

Passage

If any one strike the root of this great tree, dear, it will flow and live, 

if any one strike the middle of it, it will flow and live; 

if any one strike the top of it, it will flow and live. 

So filled with Life, with the Self, drinking in and rejoicing, it stands firm. 

But if the life of it leaves one branch, that branch dries up; 

it leaves a second, that dries up; 

it leaves a third, that dries up; 

it leaves the whole, 

the whole dries up. 

Thus indeed, dear, you must understand; said he. 

When abandoned by Life, verily, this dies; but Life itself does not die. 

For that soul is the Self of all that is, this is the Real, this the Self.

Charles Johnston. From the Upanishads. Thomas B Mosher, 1899.