A Brief Summary of Six major Darśanās in the Vedic tradition (Hinduism)

Here is my understanding of the six systems of Vedic or so-called Hindu philosophy. This is to introduce young readers to the rich philosophical tradition of India, hoping they will delve deeply if they have the interest and the time. Please send me corrections if my understanding is wrong. Thank you. 

Samkhya: There are two primordial entities: puruṣa and prakriti. There is no provision for a god in this system. Since puruṣa is unattached to everything and stands apart (state of kevala), you just have to get rid of the wrong identification of the body and the limited concept of the self and reach the state of kaivalya, realizing that the true self as puruṣa was always there. This is Jñana mārga. There is no place for bhakti (faith) or karma (action).

Mīmāmsa: This accepts Vedic gods (not the puranic gods)  but says that gods do not give us the fruits of our actions. It says that we just have to perform the rituals (karma) as ordained by the Vedās and the results will follow automatically. God is de-emphasized and therefore, Bhakti is not part of this system. Karma or action is emphasized in a limited sense of performing Vedic rituals (yagnas).

Nyāya system follows the Samkhya, except it says that logically we have to accept an Īswara who started it all. Therefore, this allows the bhakti mārga. (Vaiseṣika system is also included here) Īswara is prakriti with a form.  (Later, prakriti is equated with nirguna Brahman and Iswara with saguna Brahman)

Yoga system of Patanjali also accepts Īswara and goes on to show how to reach Him through control of the mind and meditation. This is Rāja mārga. Bhakti is also possible.

Vedanta accepts parts of each one of them.  Advaita is the first of several points of view within Vedanta. Visishtadvaita and Dvaita are the other major points of view. Adi Sankara reconciled the approaches, particularly Mimamsa, by saying Karma marga and Bhakti marga are needed (can be used) to prepare one’s mind for this journey through Jñana mārga. It also emphasizes that there is only one Atman (Brahman) occupying everything in this Universe. It emphasizes Jñana mārga by which the individual Atman merges with the Brahman.

Moksha of Advaita is called Kaivalya in Samkhya, Swarga (Kailasam or Vaikuntam) in Bhakti mārga and Apavarga in Nyāya -Vaiseṣika system.