Vinyasa Flow Yoga in a Nutshell

Source of this article : Wikipedia + personal knowledge

Principles
Vinyasa Yoga is characterized by a focus on viṅyāsa, or a dynamic connecting posture, that creates a flow between the more static traditional yoga postures. Vinyasa translates as linking and the system also implies the linking of the movement to the breath. Essentially the breath dictates the movement and the length of time held in the postures. Unlike some Hatha yoga styles, attention is also placed on the journey between the postures not just the postures themselves. The viṅyāsa 'flow' is a variant of Sūrya Namaskāra, the Sun Salutation. The whole practice is defined by six specific series of postures, always done in the same order, combined with specific breathing patterns (Free breathing with the ujjāyī sound).

Purpose of Vinyasa Yoga
The purpose of viṅyāsa is to create heat in the body, which leads to purification of the body through increased circulation and sweating. Ashtanga Vinyasa brings in the principles of Agni and inversion to purify the entire body. It also improves flexibility, as well as tendon and hard tissue strength, allowing the student to practice advanced āsanas with reduced risk of injury.

Origins of Ashtanga Vinyasa
The Ashtanga Vinyasa series is said to have its origin in an ancient text called the Yoga Korunta, compiled by Vamana Rishi, which Krishnamacharya received from his Guru Rama Mohan Brahmachari at Mount Kailash in the early 20th century. In addition, there is evidence that the Ashtanga Vinyasa series incorporates exercises used by Indian wrestlers and British gymnastics.
Krishnamacharya has had considerable influence on many of the modern forms of yoga taught today. Among his students were many notable present-day teachers such as K. Pattabhi Jois, B.K.S. Iyengar, Indra Devi, and Krishnamacharya's son T.K.V. Desikachar. Krishnamacharya was well known for tailoring his teachings to address specific concerns of the person or group he was teaching[citation needed], and a vinyasa series for adolescents is a result of this. When working under the convalescing Maharaja of Mysore, Krishnamacharya set up a shala, or yoga school in the palace grounds and adapted the practice outlined in the Yoga Korunta for the young boys who lived there. 

Vinyasa has since been thought of as a physically demanding practice, which can be successful at channeling the hyperactivity of young minds. This system can also be used as a vessel for helping calm ongoing chatter of the mind, reducing stress and teaching extroverted personalities to redirect their attention to their internal experience.