There are actually no stories in the beginning of chapters in the Bhagavad Gita. Bhagavad Gita is a conversation between Krishna and Arjuna. The passages are commentator and translator's addition before the chapter begins. These are added so as to understand the chapter better. The eighteen chapters of Bhagavad Gita are named because of the topic discussed in that particular chapter.
Chapter 1: Vishada Yoga
Chapter 2: Sankhya Yoga
Chapter 3: Karma Yoga
Chapter 4: Jnana Yoga
Chapter 5 : Karma Vairagya Yoga
Chapter 6: Abhyasa Yoga
Chapter 7: Paramahamsa Vijnana Yoga
Chapter 10: Vibhuti-Vistara-Yoga
Chapter 11: Visvarupa-Darsana Yoga
Chapter 12: Bhakti Yoga
Chapter 13: Ksetra-Ksetrajna Vibhaga Yoga
Chapter 14: Gunatraya-Vibhaga Yoga
Chapter 15: Purushottama Yoga
Chapter 16: Daiva Asura Sampat Vibhaga Yoga
Chapter 17: Shraddhatraya Vibhaga Yoga
Chapter 18: Moksa-Opadesa Yoga
If you are reading Bhagavad Gita as parayana for fulfillment of some wish, it is not necessary to read the introduction given by the translator. These are not part of Bhagavad Gita. But for reading for understanding the message and implementing it in our life, it is recommended. The message given by Krishna to Arjuna is for implementing. For implementation, you need to understand it in detail. Reading without implementation is not fruitful.
In Vivekachudamani, Adi Shankaracharya says:
śruteḥ śataguṇaṃ vidyānmananaṃ mananādapi |
nidiṃdhyāsaṃ lakṣaguṇamanantaṃ nirvikalpakam || 364 ||
Reflection should be considered a hundred times superior to hearing, and meditation a hundred thousand times superior even to reflection, but the Nirvikalpa Samadhi is infinite in its results.
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