According to Advaita Vedanta, the relationship between the self (Atman) and ultimate reality (Brahman) is that of non-duality. This means that they are not two separate entities, but rather they are one and the same. The self is not just a part of Brahman, but it is Brahman itself.

In Advaita Vedanta, the self is seen as the individual soul, while Brahman is seen as the universal consciousness or ultimate reality. However, the ultimate goal of Advaita Vedanta is to realize that the self and Brahman are not separate, but one and the same.

The self is often described as a reflection of Brahman, similar to how a wave is a reflection of the ocean. Just as the wave is made up of the same substance as the ocean, the self is made up of the same substance as Brahman. However, due to ignorance and illusion, the self identifies itself as separate from Brahman.

Advaita Vedanta teaches that the true nature of the self is pure consciousness, which is the same as the nature of Brahman. This pure consciousness is beyond the limitations of time, space, and causation, and is eternal and infinite. It is the source of all existence and the ultimate reality.

Through the practice of self-inquiry and meditation, one can realize the non-dual nature of the self and Brahman. This realization leads to the dissolution of the ego and the merging of the individual self into the universal consciousness of Brahman. This state of oneness is known as "moksha" or liberation.

In Advaita Vedanta, the relationship between the self and Brahman is likened to the relationship between a clay pot and the clay from which it is made. The pot may have a different form and function, but it is ultimately made up of the same substance as the clay. Similarly, the self may have a different identity and experiences, but it is ultimately made up of the same consciousness as Brahman.

In conclusion, Advaita Vedanta views the relationship between the self and ultimate reality as one of non-duality. The self is not separate from Brahman, but is an expression of it. Through self-realization, one can transcend the illusion of duality and experience the true nature of the self as one with Brahman.