Overview of the Six Primary Schools of Hindu Thought with Mahamuni

Due to his traveling schedule, Srila Dhanurdhara Maharaja is unable to make this evening’s sanga class. However, Maharaja has asked Mahamuni to speak on the six primary schools of Hindu thought.
From Mahamuni:

Greetings everyone,
Dhanurdhara Maharaja asked me to give this Wednesday’s talk, and provide an introduction to the six primary schools of Hindu thought. I think that the idea is that as he is discussing the Yoga tradition and applying its insights to our general sadhana, I should give some background of the key schools which have influenced the thought behind traditions like the Vaishnava Vedanta and similar schools. My plain is to discuss some of the key beliefs which they share, the key points of dispute, and what I take to be their decisive contributions to Indian thought. It may help to have a little list of the schools, so please note the following.

Mimamsa (Interpretation): focus on scriptural interpretation, particularly of the ritual portion of the Veda, and philosophy of language. Root text: the Mimamsa sutras of Jaimini.

Vedanta: focus on interpreting the Upanishads and Gita, and providing a coherent Brahman-centered metaphysics based on such texts. Root text: the Vedanta sutras of Badarayana (Vyasa)

Samkhya (Analysis): focus on identifying the fundamental features of reality under the most basic categories, generally in support of meditational practice. Samkhya thought generally pervades many other schools, and Samkhya ideas go back to the Upanishads and the Mahabharata. Root text: the Samkhya-karika of Isvarakrishna.

Yoga (Spiritual discipline): focus on the psychology of spiritual discipline for the sake of meditational practice. Like Samkhya, it basic yoga notions pervade many of the other schools, and goes back to the Upanishads and Mahabharata. Root text: the Yoga-sutras of Patanjali.

Nyaya (Logic): focus on the theory of knowledge, and logic. This school wants to defend the Vedic culture, the existence of God, and a basic realist picture of the world against competing schools like Buddhism. Other schools borrow from its logical theory. Key text: the Nyaya sutras of Gautama.

Vaisheshika (Atomism): a realist school which defends a metaphysical picture somewhat different from the Samkhya. It becomes subsumed into Nyaya around 1000 CE. Root text: the Vaisheshika sutras of Kanada.

Generally the six schools are grouped into three sets of two sister schools, as above. Aside from these, there were influential Hindu schools like the Grammarian school, and non-Hindu schools like Buddhism, Jainism and Charvaka (the materialist tradition).
Thanks.
Muni