Adi Shankaracharya, a renowned Hindu philosopher and theologian, is considered to be one of the most influential figures in the development of Advaita Vedanta, a school of Hindu philosophy. He is also known for his disciples who carried on his teachings and spread them across India. Some of the key teachings of Adi Shankaracharya's disciples include the following:

1. Oneness of the Self: Adi Shankaracharya's disciples emphasized the concept of Advaita or non-dualism, which states that the ultimate reality is one and the individual self (Atman) is not separate from the universal self (Brahman). They taught that the true nature of the self is pure consciousness and realizing this oneness is the path to liberation.

2. Illusion of the World: Adi Shankaracharya's disciples taught that the world is an illusion (maya) and the true reality lies beyond it. They believed that the world is constantly changing and is not the ultimate truth. By understanding this illusion, one can attain liberation from the cycle of birth and death.

3. Importance of Guru: Adi Shankaracharya's disciples stressed the importance of a guru or spiritual teacher in one's spiritual journey. They believed that a guru is essential for guiding an individual towards self-realization and liberation. They also emphasized the need for surrendering to the guru and following their teachings with utmost devotion.

4. Practice of Yoga: Adi Shankaracharya's disciples believed in the practice of yoga as a means to attain self-realization. They taught various forms of yoga, such as Jnana Yoga (path of knowledge), Bhakti Yoga (path of devotion), and Karma Yoga (path of action), as ways to purify the mind and reach the ultimate truth.

5. Non-attachment: Adi Shankaracharya's disciples emphasized the importance of non-attachment (vairagya) to worldly desires and possessions. They believed that attachment leads to suffering and hinders one's spiritual progress. By cultivating non-attachment, one can attain a state of inner peace and detachment from the material world.

In conclusion, Adi Shankaracharya's disciples carried on his teachings and spread the message of Advaita Vedanta across India. They emphasized the oneness of the self, the illusion of the world, the importance of a guru, the practice of yoga, and non-attachment as key teachings for spiritual liberation. Their teachings continue to inspire and guide seekers on the path of self-realization even today.