In Natyashastra by Bharata Muni, what are the main points (or the summaries) of the first, sixth, and seventh chapters?

These sections lay out how to understand the role of emotional states in dramatric performance. The key terms here to understand are bhava and rasa.  A bhava is a kind of mood or experience that comes with a scene or action, while a rasa is the inner feeling that the drama is protraying. There are eight rasas: love, humor, anger, compassion, disgust, horror, courage, and wonder. The theory is that it is through the signs and actions of dance and acting that the audience experiences the feelings the actor intends.

Since the first chapter deals with creation, and the suggestion that drama constitutes a "fifth Veda," the implication is that once can experience transcendent or religious states through drama. Many plays enacted scenes taken from lore about the gods, heroes, and other quasi-divine beings from Indian lore. Since the Vedas were barred to the lowest classes, these dramas were a way to experience the stories associated the Vedic hymns.