Origin of Ashtanga Yoga series is basically a very old text called the "Yoga Korunta", collected by Rishi Vamana. Originally Rishi Krishnamacharya received this text from his Guru Rama Mohan Brahmachari at Mount Kailash. Asthanga Yoga contains record of many different combinations of asanas, and also highly unique knowledge on mudras, vinyasa, bandhas, drishti, and philosophy. As summarized by the knowledgeable Patanjali in the Yoga Sutra, Ashtanga yoga is "eight-limbed yoga". According to Patanjali, the course of inner sanitization for revealing the self-identity is consists of the eight divine practices:

Yama (moral codes)
There are lots of interpretation about the yamas, like Bhagavata Purana allocate 12 yogic restraints, Parashar Smriti puts forward ten for Yama. But in Patanjali`s Yoga Sutra only five restraints are described that are also recognized as the great universal vows.
Niyama (self-purification and study)
Niyama tells how we relate with our internal world and ourselves. The Niyamas are all about self-regulation that helps us in maintaining a positive environment.
Asana (posture)
Asana mean achievement of a constant and relaxed sitting posture to make meditation easy. Asana also helps in evaluating and harmonizing the fundamental formation of the body that is why they have a variety of therapeutic uses.
Pranayama (breath control)
Pranayama is all about overprotecting or controlling the life force. The training of pranayama helps in connecting the prana in and around us. By deepening and extending it, pranayama show the way of inner peace.
Pratyahara (sense control)
Pratyahara involves correctly controlling the senses and departing beyond them in place of just closing and suppressing them. Generally it practiced with mantra meditation and imagination techniques.
Dharana (concentration)
Dharana contain developing and expanding our concentration power. There are many ways of controlling our attention and mind-fixing abilities, such as focussing on the chakras or turning inwards.
Dhyana (meditation)
Dhyana is nothing but the state of meditation, when the mind achieves the capability to maintain its attention without getting troubled.
Samadhi (contemplation|)
Samadhi, is the capability to become one with the exact self and combine into the object of meditation.