Summing up the teaching of Upanishad Dr Radhakrishnan says
God’s dwelling place is in the heart of man. The inner immortal soul and the great cosmic power are one and the same. Brahman is Atman and Atman is Brahman.
We have to remember that the highest religion of the Upanishads, which insists on meditation and morality and worship of God in spirit and truth, is not encumbered by such traditional dogmas and miracles as still hang upon the skirts of other religions. Its central principle that there is one supreme reality that manifests itself in the universe is not asserted as a dogma. It is the ultimate truth at which it is possible for human understanding to arrive. The progress of science and philosophy does not conflict with it but only confirms it.
The Upanishads, though remote in time from us, are not remote in thought. They disclose the working of the primal impulses of the human soul which rise above the differences of race and of geographical position. At the core of all historical religions there are fundamental types of spiritual experience though they are expressed with different degrees of clarity. The Upanishads illustrate and illuminate these primary experiences.
The Upanishads deal with questions which arise when men begin to reflect seriously and attempt answers to them which are not very different, except in their approach and emphasis from what we are now inclined to accept. This does not mean that the message of the Upanishads, which is as true today as ever, commits us to the different hypotheses about the structure of the world and the physiology of man.
We must make distinction between the message of the Upanishads and their mythology. The latter is liable to correction by advances in science. Even this mythology becomes intelligible if we place ourselves as far as possible at the viewpoint of those who conceived it.
Anyone who reads the Upanishads in the original Sanskrit will be caught up and carried away by the elevation, the poetry, the compelling fascination of the many utterances through which they lay bare the secret and sacred relations of the human soul and the ultimate reality. When we read them we cannot help being impressed by the exceptional ability, earnestness and ripeness of mind of those who wrestled with these ultimate questions. These souls who tackled these problems remain still and will remain for all time in essential harmony with the highest ideals of civilization.
(Source: from Preface to The Principal Upanishads by S. Radhakrishnan )