YAMA : five restraints or disciplines
nonhurting; truthfullness; nonstealing; control of appetites; non grasping.......

NIYAMA : five ways of practicing a healthy mental state
purity; contentment; austerity; study; surrender....

ASANA
postures...ie; yoga class...

PRANAYAMA
controlled breathing....

PRATYAHARA
withdrawal of the senses....

DHARANA
concentration; contemplation....

DHYANA
still mind meditatiom....

SAMADHI
enlightenment.....
THIS CANNOT BE TAUGHT....ONLY EXPERIENCED...THERE ARE NO WORDS TO EXPLAIN TRUE SAMAHDI.

8 LIMBS = ASHTANGA YOGA
There has been some confusion in the west about the definition of Ashtanga yoga....some people confuse Ashtanga yoga with Vinyasa or flow / dance yoga...
Actually, ASHTANGA YOGA is when ALL of the 8 LIMBS of YOGA (listed above ) are taught.

Sadly this is rare in most yoga schools today, as an emphasis on physical postures seems to be more popular, thus the philosophy and breath work has been somewhat forgotten....