Hindus have 6 philosophies called Dharshanas and believe it or not, Bhagavad Gita starts and ends with Sankhya Philosophy. Other philosophies that are mentioned in the Bhagavad Gita are Yoga and Vedanta. By the way, Bhagavad Gita only mentions three Vedas (Rik, Sama, Yajur). No mention of the Athrava Veda.

The six philosophies known as Darshanas are as follows: Mimamsa (beginning of the Vedas) ; Samkhya; Yoga; Nyaya, Vaisheshika, Mimamsa, Vedanta (end of Vedas).

Vedanta was further divided into two – Advaida (only one) and Dwaita (two).

Vedanta is mentioned few times in the Bhagavad Gita in verses 13:5 and 18:12.

Sankhya or Samkhya is a dualistic philosophy founded by Rishi Kapila which is expounded by Isvara Krishna (6th Century AD) in his work, the Samkhya Karika.

Sankhya or Samkhya philosophy consists of two realities Purusha (consciousness or energy) and Prakruti (matter) ——cosmic dualism. No mention about God.

From Purusha, Prakruti emerges and at the end merges back with Purusha. This is cyclic and never ending according to Kapila. Lord Krishna repeated this fact in the verse (Bhagavad Gita Chapter 9:7 )

Prakruti is governed by three Gunas —— Sattvic, Rajastic and Tamasic.

1 - Lord Krishna begins his advice to Arjuna mentioning Sankhya philosophy in this verse. (Bhagavad Gita --2:39)

2 - Lord Krishna said: “People who follow Sankhya philosophy and people who follow Karma Yoga have the same result." (Bhagavad Gita --3:3 )

3 - Lord Krishna said: “Sankhya and Yoga are one." (Bhagavad Gita -- 5:4,5 )

4 - Lord Krishna discusses Eight basic elements according to Sankhya. (Bhagavad Gita --7:4 )

5 - Arjuna wants to know about Purusha and Prakruti.(Bhagavad Gita --13:1)

6 - Purusha and Prakruti (Sankhya Philosophy) aspects of Sankhya are discussed in these verses. (Bhagavad Gita -- 13:20 to 23)

7 - Lord Krishna said: "Among Siddhas (perfected beings) I am the sage Kapila (founder of Sankhya philosophy) (Bhagavad Gita --10:26 )

8 - Gunas (Satwa, Rajo, Tamo) are part of the Sankhya Philosophy.

9 - Chapter 14 of the Bhagavad Gita is called Gunatraya Vibhaga Yoga means the “Yoga of the division of three Gunas”. In this chapter Lord Krishna analyses Gunas in very minute detail in 27 verses.