Texts on yoga philosophy go back to the 8th century BCE. Our modern styles of yoga are commonly based on the texts of Hatha Yoga Pradipika, which are believed to originate in the 15th Century. The first yogis travelling through the western world focused on practises of pranayama (breath control) and meditation.
Only in the mid 1920s, modern asana (postures) practises as we know them today began to develop through various teachers. Swami Satyananda, who first came to Australia in the early 1970s, continued this ancient tradition handed down through a long lineage of Indian yogis.
The yoga I teach is a continuation of Swami Satyananda's teachings.
Further reading
If you are interested in finding out more on the history of Yoga, I can recommend a great article posted on Yoga Journal, entitled The roots of Yoga: Ancient and Modern.