“Ashtanga Yoga is an ancient system of Yoga that was taught by Vamana Rishi in the Yoga Korunta. This text was imparted to Shri T. Krishnamacharya in the early 1900’s by his Guru Rama Mohan Brahmachari, and was later passed down to Pattabhi Jois during the duration of his studies with Krishnamacharya, beginning in 1927.” Shri T. Krishnamacharya is one of the most distinguished yogis of the 20th Century. Shri Pattabhi Jois died in 2009, but his institute in Mysore, India, is still open.
Ashtanga consists of eight limbs of yoga. These are:
Yama – moral codes
Niyama – self-purification and study
Asana – poses
Pranayama – breath control
Pratyahara – sense control
Dharana – concentration
Dhyana – meditation
Samadhi – self-realization
What distinguishes Ashtanga from any other yoga is the synchronicity of the movement and breathing system. The breath is called ujjayi. You draw the breath in and out of the nostrils while the sound comes from your throat. As a practitioner you also use bandhas, bandha means “lock”. There are three bandhas, and the result of applying a bandha is to unlock the lifeforce. Each asana has a gaze point at which to focus, these are called dristis, and there are nine of them.
I recommend going to a class, there is a list of certified teachers here. A good teacher will help you progress through the various poses. It can take many months, even years, to be able to do the primary series. After you complete the primary series you start on the advanced series, I never got that far.
If you also want to practice at home it might be helpful to consult John Scotts’s book Ashtanga yoga – The Definitive Step by Step Guide to Dynamic Yoga. The book has a foreword by Shri Pattabhi Jois and it was the only book I used. There are more suggestions of books for home practice here.