Short answers, pulled from the story.
The Bhagavata Purana, also called the Srimad Bhagavatam, is one of Hinduism's eighteen major Puranas and a central text of Vaishnavism. It consists of twelve books, 335 chapters, and 18,000 verses, and is widely recognized as the most influential of the Puranas. It is also referred to as the Fifth Veda in Vedic literature.
Modern scholarship dates the composition of the Bhagavata Purana to between 500 CE and 1000 CE. A version of the text existed by 1030 CE, when it is mentioned by al-Biruni and quoted by Abhinavagupta. Many scholars date its final redaction to the 9th or early 10th century.
The Bhagavata Purana is written in Sanskrit. It was the first Purana translated into a European language, with a French translation of a Tamil version appearing in 1788, introducing many Europeans to Hinduism during the colonial era.
The tenth canto is the most popular and widely studied part of the Bhagavata Purana. It contains approximately 4,000 verses and focuses on the life and divine play of Krishna, including his childhood in Vrindavan and his adult activities in Mathura and Dvaraka. It has been translated and published separately from the rest of the text.
The Bhagavata Purana synthesizes Bhakti Yoga, Dvaita Vedanta, Samkhya, Yoga, Vedanta, and Advaita Vedanta. The scholar Sheridan describes its resolution of these traditions as Advaitic Theism, a both/and solution to whether God is transcendent or immanent. Bryant summarizes it as a mixture of Vedanta terminology, Samkhyan metaphysics, and devotionalized Yoga practice.
Canto 10 of the Bhagavata Purana is regarded as the inspiration for classical dance styles including Kathak, Odissi, Manipuri, and Bharatnatyam. The five chapters of the Rasa Panchadhyayi in Canto 10 form the basis for many Ras plays. Bryant states that the Bhagavata has inspired more derivative literature, poetry, drama, dance, theatre, and art than any other text in the history of Sanskrit literature, with the possible exception of the Ramayana.