Atman (or paramätman, the highest Self), for Advaita Vedanta is that pure, undifferentiated self-shinning consciousness, timeless, spaceless, and unthinkable, that is not different from Brahman and that underlies and supports the individual human person.

Ätman is pure, undifferentiated, self-shinning consciousness: It is a supreme power of awareness, transcendent to ordinary sensemental consciousness, aware only of the Oneness of being.

Atman is that state of conscious human being wherein the division of subject and object, which characterize ordinary consciousness, are overcome.   Nothing can condition this transcendental state of consciousness:   among those who have realized it, no doubts about it can arise.   Atman is thus void of differentiation,  but for Advaita it is not simply a void:  it is the infinite richness of spiritual being.

In later Advaita, as we have noted earlier, a distinction is made between two types or kinds of spiritual experience related to transcendental consciousness:  that of savikalpa samadhi, the borderline experience, as it were [...] and that of nirvikalpa samadhi, the pure experience of Reality.

Savikalpa samadhi means "determinate" spiritual experience.  In it an awareness of duality is absent, but unlike susupti, the deep-sleep state, the emphasis here is not so much on the absence of duality as it is on the presence of non-duality. Whereas in susupti the self is still a knowing subject, although there is nothing there as such to be known, in savikalpa samadhi the self is aware only of the presence of Reality.  In susupti all the phenomenal activities self are suspended in a kind of serene blank; in savikalpa samadhi they are concentrated on the Real. In susupti the self is still very much the jiva; in savikalpa samadhi the self is passing into the Atman.

Nirvikalpa samadhi is the consumation of the process. It is the pure "indeterminate" intuition of non-duality.  In savikalpa samadhi the Self is aware of Reality; in nirvikalpa samadhi it is Reality.