Adi Shankaracharya, also known as Shankara, was a great Indian philosopher and theologian who lived in the 8th century. He is considered to be the proponent of Advaita Vedanta, a school of Hindu philosophy that emphasizes the concept of non-dualism. According to Shankara, the ultimate reality is the universal self, also known as Brahman, and the individual self is a mere reflection of this universal self.

Shankara believed that the individual self, or the jivatma, is not separate from Brahman, but is rather a manifestation of it. He explained this relationship between the individual self and the universal self through the concept of maya. Maya, according to Shankara, is the illusion of duality that makes us perceive ourselves as separate from Brahman.

Shankara argued that the individual self is limited by its identification with the body, mind, and ego. These are all temporary and constantly changing, and therefore cannot be the true self. The true self, according to Shankara, is the universal self, which is eternal, unchanging, and all-pervading.

To understand this relationship better, Shankara used the analogy of a wave and the ocean. Just as a wave is a temporary manifestation of the ocean, the individual self is a temporary manifestation of the universal self. The wave may think it is separate from the ocean, but in reality, it is nothing but the ocean itself. Similarly, the individual self may think it is separate from Brahman, but in reality, it is nothing but Brahman itself.

Shankara also emphasized the importance of self-realization in understanding this relationship. He believed that through self-inquiry and contemplation, one can realize the true nature of the self and break free from the illusion of maya. By realizing that the individual self is nothing but a reflection of the universal self, one can attain liberation from the cycle of birth and death.

In addition, Shankara also stressed the role of karma in this relationship. He believed that our actions, thoughts, and desires are all influenced by maya, and it is only through self-realization and detachment from these worldly attachments that one can truly merge with the universal self.

In conclusion, Adi Shankaracharya explained the relationship between the individual self and the universal self as one of non-duality. He believed that the individual self is a mere reflection of the universal self and that the illusion of duality is what separates us from realizing our true nature. Through self-inquiry, detachment, and realization, one can understand and experience the oneness of the individual self and the universal self.