Ashtanga Yoga is a systematic method devised by Sri K Pattabhi Jois with reference to the teachings of his teacher Sri Krishnamacharya, Krishnamacharya's teacher, Ramana Mohan Brahmachari and the teachings of an ancient sage known as Rishi Vamana which were given in an ancient text known as the Yoga Korunta.

We know nothing about the ancient sage Vamana except what appears in legends. We know very little about Ramana Mohan Brahmachari, except that he lived in Tibet at the foot of Mount Kailash. Krishnamacharya studied with him for seven years and then returned to India, settling eventually in the southern indian city of Mysore.

Sri K Pattabhi Jois was born in South India not far from Mysore and commenced studies with Krishnamacharya in 1927 as a twelve year old boy. He became a professor at the Maharaja's Sanskrit College and taught yoga from 1937 onwards. Guruji passed away in May 2009 and the yoga shala in Mysore is run by his daughter Saraswathi and grandson Sharath, while his grandaughter Shemee teaches in Bangalore and his son Manju travels the world spreading this same message of yoga.

Sri K Pattabhi Jois
Sri K Pattabhi Jois was born in 1915 in the South Indian village of Kowshika. His father was an astrologer and priest. As a twelve year old boy he attended a demonstration and lecture given by Krishnamacharya at his high school in Hassan. When Guruji  saw the yoga demonstration he was immediately inspired to take up yoga practice. He went to meet Krishnamacharya the next day and commenced his yoga practice.

Guruji moved to Mysore to study at the Sanskrit college where he became a professor and was invited by the Maharaja to start a Yoga department. He continued his studies with Krishnamacharya for 25 years and was instructed by him to teach according to the method described in the Yoga Korunta without changing anything. This he continued to do for more than seventy years.

see Guruji's site for more details

Manju Jois - New York 2000
GUY: Manju, how old were you when you started to practice?

MJ: Oh, let’s see, I was seven-years old. Mmmm. It was just like a game for me, you know, just to watch and then you try to do it because it’s fun. It was not done seriously, he was not making me do things. We just go voluntarily and start playing with the postures, that’s all.

GUY: When did he start teaching you formally?

MJ: Formally when I was twelve-years old. Then we had to practice everyday – in the morning and evening. He started teaching me and my sister individually giving us a private lesson. That’s how it all started.

Saraswathi Rangaswami - An interview with Guruji´s daughter
Profile of KP Jois by Eddie Stern
From Hinduism Today  January/February 2001

Krishna Pattabhi Jois was born on the full moon day of July, 1915, Guru Purnima day. His ancestral village, Kowshika, near Hassan in Karnataka State, is inhabited by maybe 500 people and has one main street.
Sri Tirumali Krishnamacharya was one of the most influential and innovative yoga teachers of the twentieth Century. Not only was he a master of yoga, but he held the equivalent of doctorates in seven different fields including ayurveda, law and philosophy.

In the last century, the Ashtanga Yoga method was imparted to Krishnamacharya by a tibetan yogi called Sri Ramamohan Brahmachari.

Krishnamacharya heard of the yogi adept living in Tibet at the foot of Mt Kailash while he was studying in Varanasi in northern India. In 1915 he travelled on foot for several weeks looking for him. There, on the shores of lake Mansovar, he found Ramamohan Brahmachari living in a cave with his wife and children. On seeing Krishnamacharya's earnest desire to learn, Brahmachari agreed to take him on as a student.
Krishnamacharya - The King and the Young Man
He lives quietly, like a full pot (empty pots are proverbially noisy), shines steadily like a bright lamp of knowledge. Working daily at his pursuit of knowledge, he lives the life of a rshi of old, though he lives in his home with his wife and family...

The King and the Young Man - by "Hastam"
in Kalaimagal, Pongal, 1984
(translated by Bert Franklin and S. Venkataraman)
An Interview with Sri T Krishnamacharya

Important figures in the evolution of Ashtanga Yoga
The modern day practice of Ashtanga Yoga represents the confluence of a number of streams of hindu philosophy, practice and spirituality. A number of important figures feature prominently in the evolution and representation of this particular method, but many others have played their part too.

Krishnamacharya from Wikipedia
Sri Tirumala Krishnamacharya (1888–1989) was born on November 18 in Muchukundapuram, in Chitradurga district of Karnataka state in India and lived to be over a hundred years old. His parents were Sri Tirumala Srivinasa Tattacharya, a well-known teacher of the Vedas, and Shrimati Ranganayakamma and he was the eldest with two brothers and three sisters.