Yoga means Union & Ashtanga yoga literally means "eight-limbed yoga," as outlined by Patanjali in the Yoga Sutras. The eight limbs of Ashtanga Yoga are:

Yama - moral codes   
Niyama - self-purification and study
Asana - posture
Pranayama - breath control
Pratyahara - sense control
Dharana - concentration
Dhyana - meditation
Samadhi - absorption into the Universal 

Ashtanga yoga is a traditional form of Yoga that involves synchronising the breath with a progressive series of postures— a process producing intense internal heat and a profuse, purifying sweat that detoxifies muscles and organs. The result is improved circulation, a light and strong body, and a calm mind.

There are two ways Ashtanga can be learnt; in a lead class (with the verbal lead of the teacher) or 'Mysore Style' teaching refers to the traditional method of teaching whereby students are taught in a group setting but practice independently (without the vocal lead of a teacher) at their own level deemed appropriate by the teacher. Having learnt the Surya Namaskara's (sun salutations), traditionally postures are given one by one to the student when the teacher feels they are ready, leading them to gradually complete the series.

In 1916 a man named Sri Tirumalai Krishnamacharya went to study yoga in the Himalayas. There he met his future guru Sri Ramamohanem Brahmacharim and spent seven and a half years of his life with him. During this time he studied the roots of what would later become the Ashtanga yoga system. He then went on to teach in Mysore, India. Krishnamacharya taught great teachers, some of whom went on to popularise Yoga all over the world, such as Pattabhi Jois, BKS Iyengar, BNS Iyengar (who is still alive and teaching in Mysore, India) & Indra Devi.

Ashtanga Yoga is traditionally practiced early in the morning, 6 days a week, with one day of rest. Traditionally there is no practice to be done on new moon and full moon days, this is because there are increased energies on these particular days, also, scientifically the moon controls the movement of the sea, we are made of water, therefore on these days we are more susceptible to injury and more open to physical and mental afflictions.