Yoga was 1st mention in the Vedas, during the Pre classical era, thousand of years ago.
Around 200 BC, classical era. Pantajali wrote the Yoga Sutras, which are the same ones we study today.
Reaching the modern era, between 200-300 years ago we have Krishnamacharya the father of Modern Yoga.
Krishnamayaria spent 7 1/2 years in a cave learning yoga with Brahmachari. His ultimate purpose was to still the fluctuation of the mind. His conception of yoga was teach what is appropriate for the individual. He became friends with the Mysore Maharaja, which facilitated him to have a school in Mysore.
He had recognized students, including Pattabhi Jois and BKS Iyengar among others.
Pattachi Jois is the father of Ashtanga-Vinyasa Yoga. He created a method to teach yoga including strict routine and discipline, he got inspire by teaching young boys. He wanted to physical exhaust them to calm their mind.
Ashtanga yoga emphasis the Asana to later be able to meditate.
Ashtanga students are gradually led through a set sequence of postures step by step. There are 6 series, regular people usually reach the 2nd series. The rest are so advance that only a handful of people an perform them.
I hope this little summary helps you research more about Ashtanga yoga or Yoga in general.
So next time you finish your practice you can take 1 minute and thank all the teachers that passed us their knowledge for thousand of years, so we can benefit from the practice.