Recall the teachings of Chapter X.
Then the final statement in Verse 40:
In Chapter XI, Shree Krishna demonstrates this by revealing to Arjun one of his divine & Universal representations.
In Chapter XIII, Shree Krishna provides a metaphysical basis for the teachings of Chapter X by linking his teachings with the ancient Samkhya approach. In this context, Shree Krishna describes himself as क्षेत्रज्ञ or Kshetradnya.
The easiest way to understand the concept of क्षेत्र (Kshetra) is a literal one. The word means physical space or existence. In the context of Chapter XIII, the word Kshetra means the physical entities. This is what the Samkhya School calls प्रकृति or Prakruti.
The concept of क्षेत्रज्ञ or literally one who understands & controls क्षेत्र is linked later in this Chapter to परम-आत्मन (Param-Atman) or the Universal Soul and the Samkhya concept of Purush (पुरुष).
The various Upa-Nisad were composed by different Rushi or Sages at different times. In these Upa-Nisad, the authors laid out philosophical concepts as they saw them. It was Sage व्यास (Vyaas) or बादरायण (Baadaraayan) who created a composite path among the various Upa-Nisad with his great treatise called Brahma-Sutra (ब्रह्म-सूत्र) or Vedanta-Sutra (वेदांत-सूत्र) or simply Baadaraayan-Sutra.
In Verse 4 of Chapter XIII, Shree Krishna specifically refers to Brahma-Sutra as the clarifying entity of the various Upa-Nisad written by various Rushi.
From Verses 5 onwards, Shree Krishna lists the principles of Prakruti as specified by the Samkhya School – the Aham-Kaar, the five great substances (पंच महाभूत) , the five Indriya etc. As He explains these properties, He discusses the concept of Dnyaan or the understanding of the duality between the physical properties vs. the Nir-Gun, Eternal Atman.
In Verses 24-25, Shree Krishna explains that all the Three Paths to Liberation enable people to break the cycle of life & death.
In other words, you can transcend death with Samkhya Dnyaan, with Karma-Yog or with Devotion or Bhakti.
The other Verses summarize the teachings in simpler declarative verses:
This the synthesis of the Samkhya and Vedant-UpaNisad approaches. This is a more elaborate exposition of the statement of:
Before discussing the next verse, allow us to take you back to Chapter IV and the concept of Non-Attachment of Actions to the Doer. We discussed this at some length in our article Reflections on the Bhagwat Geeta – Chapter IV, Secion II . Specifically recall:
In this Verse 14 of Chapter 4, the “I” is Shree Krishna. Now read Verse 31 of Chapter XIII.
In this Verse, Shree Krishna uses the term Param-Atman instead of the “I” term he used in Verse 14 of Chapter IV. This is the meaning of his exhortation to Arjun in Verse 2 to understand that He, Shree Krishna is the क्षेत्रज्ञ, the Param-Atman of all क्षेत्र or created entities.
The above discussion shows that this Chapter is aptly named as क्षेत्र- क्षेत्रज्ञ-विभाग-योग or Kshetra-Kshetradnya-Duality-Yog.
Thus Endeth Chapter XIII named Kshetra-Kshetradnya-Duality-Yog (क्षेत्र- क्षेत्रज्ञ-विभाग-योग of Shree Bhagwat Geeta, of the Upa-Nisad (उप-निसदत्सु) , of the Yog-Shaastra (योग शास्त्र) of Brahma-Vidyaa (ब्रह्म विद्या), of the dialog (संवाद) between Shree Krishna & Arjun.