Ashtanga Yoga

Ashtanga Yoga is the yoga of the eight limbs

(ashta= eight; anga= limbs; yoga= union)

Patanjali (sage that lived in between V e IV century BC) describes the eight limbs:

Yama – observances and behaviors which regulate how we relate to others
Nyama – commitments to ourselves, and principles that we should follow in our daily life
Asana – physical posture/ control of the body
Pranayama – control of the breath
Pratyahara – withdrawl of the senses
Dharana – concentration
Dhyana – meditation
Samadhi – realisation of the Self

The first four limbs are externally oriented. The last four limbs are to be internally experienced.
 
To practice Ashtanga Yoga means practicing all the disciplines previously described (in but specially out the yoga mat). It will be of great importance knowing each and every single of this limbs once they are intimately connected leading to the ultimate of this that is Samadhi
 
Because of the fact that they are essential to the asana practice (and to our daily life/routine), the first two are described in  more detail:

Yama

Ahimsa – non-violence
Satya – truth
Asteya – non-stealing
Brahmacharya – fidelity to one partner/ sexual energy control
Aparigraha – non-greediness/ detachment

Nyama:

Sauca – internal and external cleanliness
Santosha – self contentment
Tapas – self discipline/austerity
Svadhyaya – self study/ ancient texts study/ study with a teacher.
Isvara pranidhana – Devotion to a supreme force (yoga practice is a spiritual one, not merely a physical exercise; the effort is done as a way of reaching a greater spiritual knowledge).

Method

The method is a dynamic one, based on the synchronisation of the breathing and the progressive series of asanas (vinyasa krama). This combines fluid and sequencial movements with all the attention turned internally.
 
Through the self-practice and self-observation what is developed is a widening of consciousness, rather than a dominant self-critical attitude. “Consciousness” tends to overcome the “mind/Ego”. This last ability is manifested through the focus in the fluidity of the natural breathing. Breathing is the vehicle through which the body/mind are in observation and become purified and can eventually be transcended.