The Advaita Vedaanta is without doubt the most significant philosophical scheme born on the soil of India. It is a system of great speculative daring and logical subtlety, which in its austere intellectualism marches on indifferent to the hopes and beliefs of man. While Max Muller thinks that, "metaphysical speculation has reached its acme", in this school, another European admirer observes : "The doctrine advocated by Shankara is from a purely philosophical point of view and apart from all theological considerations, the most important and interesting one which has arisen on Indian soil; neither those forms of Vedaanta which diverge from the view represented by Shankara, nor any of the non-Vedaantic systems can be compared with the so called orthodox Vedaanta in boldness, depth and subtlety of speculation". Professor Radhakrishan only expresses the popular opinion when he says : "It is impossible to read Shankara's writings , packed as they are with serious and subtle thinking, without being conscious that one is in contact with a mind of a very fine penetration and profound spirituality … His philosophy stands forth complete, neither needing a before nor an after … whether we agree or differ, the penetrating light of his mind never leaves us where we were". Advaita holds the first place in Indian philosophy and from the day it was born, its influence remains unrivalled in the philosophical and spiritual milieu of India.
The Maandukya Kaarikaas of Gaudapaada (6th century CE), represents the first formal exposition of Advaita. Gaudapaada was the paramaguru of Shankara i.e., the guru of Shankara's guru Govinda.
Shankara's main works are the commentaries on the principal Upanishads, the Bhagavat Geetha and the Vedaanta Sutras. Upadeshasaahasri, Vivekachoodaamani, Aptavajrasoochi, Atmabodha, Mohamudgara, Dashasloki, Aparoksaanubhuti, the commentaries on Vishnusahasranaama and Sanatsujaatiya are works attributed to him. The soul stirring hymns composed by him are Bajagovindham, Saundaryalahari, Lalitaasahasranaamam, Sivaanandalahari, Anandalahari, Dakshinaamurti Stotram and Harimiide Stotram.
Mandana Mishra was a disciple of the great Miimaamsakaa Kumarilla Bhatta. He was defeated in a debate by Shankara and was converted to the Advaita fold. His work on Advaita is the Brahmasiddhi. The identification of Mandana with Shankara's foremost disciple Sureshvara is not confirmed. Sureshvara's main work is the Naishkarmyasiddhi. He has also written vaarttikas on several of Shankara's works.
Vaachaspati Mishra's Bhaamati, Padmapaada's Panchadipikaa and Anandagiri's Nyaayanirnaya were composed immediately after Shankara's time. Amalaananda (13th century CE) has commented on the Bhaamati in his Kalpataru, which itself was commented upon by Appaya Dikshita (16th century CE) in his Kalpataruparimaala. In his Siddhaantalesha, Appaya sums up the divergent developments of Advaita. Prakaashaatman (12th century CE) has commented upon Padmapaada's Panchadipikaa, in his Panchadipikavivaarana. A gloss on Prakaashaatman's work is Vidyaaranya's Vivaaranaprameyasamgraha. Vidyaaranya (14th century CE) generally identified with Maadhava is also the author of Panchadashi and Jeevanmuktiviveka. Sarvajnaatmamuni (9th century CE) made a general survey of Shankara's views in his Samkshepashaariraka.
The Khandanakhandakhaadya of Sri Harsha (11th century CE) is the greatest work on Advaita dialectics. Citsuhka wrote a commentary on it called the Citsukhiyam. Another work of his on the same lines is the Tattvapradipika. Madhusudhana Saraswati (16th century CE) defends the Citsukhiyam against the attacks of the Dvaitins in his Advaitasiddhi. Brahmananda's Guruchandrikaa defends Advaitasiddhi against further criticisms. Shankara Mishra and Ragunaatha too have commented on the Khanadanakhandakhaadhya. Vedaantaparibhaasha by Dharmaraaja (16th century CE) is an excellent manual on logical metaphysics. Dharmaraaja's son Ramakrishna has commented on it in his Sikhaamani and Amaradaasa's Maniprabha is an useful gloss on it.
Sadaananda's Vedaantasaara (15th century CE), Advaitananda's Brahmavidhyabharana (16th century CE), Govindananda's Ratnaprabha, Prakaashananda's Siddhaantamuktaavali, Sadaananda's Advaitabrahmasiddhi and Lakshmidara's Advaitamakaranda are other Advaita works of considerable importance.