Shankaracharya with disciples
Painting by Raja Ravi Varma
The root sutra of Yoga is Patanjali’s Yoga Sutra. The dualistic metaphysics of Samkhya underpins the practical and action based psychology of Yoga.
The root sutra of Nyaya, the school of logic and argumentation, is Gautama’s Nyaya Sutra. The root sutra of Vaisheshika, which is an atomistic tradition, is Kanada’s Vaisheshika Sutra. In the ancient age, Nyaya and Vaisheshika were separate schools. But in the early Middle Ages, they started coming together, forming a single syncretic school, Nyaya-Vaisheshika, which specialized in logic, argumentation, epistemology, and metaphysics.
The root sutra of Mimamsa, the school of scriptural exegesis, is Jaimini’s Mimamsa Sutra. The school of Vedanta (also known as Uttara Mimamsa) focuses on the teachings of the later Upanishadic texts and its root sutra is Badarayana’s Brahma Sutra.
For every root sutra, there is a bhasya (commentary), which comes at a later stage.
For Patanjali’s Yoga Sutra, the bhasya is Vyasa’s Yogabhasya. For Gautama’s Nyaya Sutra, the bhasya is Vatsyayana’s Nyayabhasya. For Kanada’s Vaisheshika Sutra, the bhasya is Prasastapada’s Padartha-dharma-saṅgraha. For Jaimini’s Mimamsa Sutra, the bhasya is Shabara’s Shabarabhashya. For Badarayana’s Brahma Sutra, the bhasya is Adi Shankaracharya’s Brahma Sutra Bhasya.