I dare to be bold to give views about AT basics, encouraging discussions and additions to it.
Personally, I like the simple approach of awareness, inhibition, direction and intention to describe the basics. Learning about awareness includes Alexander's ideas of faulty sensory appreciation and the conditions and manner of use, and body mapping. Directing requires knowledge about the primary control, the relation between head, neck and back. Inhibition helps understanding the difference between end-gaining and the means-whereby. Intention enables us to experience psycho-physical unity.
This short wrap-up comes close to the list of basic AT terminology I found on the web. However, Alexander and other teachers developed specific methods that help learning the technique, such as the whispered aah, monkey, lunge and hands on the back of the chair, which might (or might not) part of the basics.