The ‘style’ of Karate we learn at the Dojo is called “Matsubayshi Shorin-Ryu”. You can consider “Shorin-Ryu” the root style, and “Matsubayshi” one of the branches of Shorin-Ryu.
Shorin-Ryu is one of the oldest styles of Karate and originated from the small Japanese island of Okinawa.
The very first Kata we learn is called “Fugyugata Ichi”, Ichi meaning “one” or first in this case.
You can find out more information about Matsubayshi Shorin-Ryu by reading this wiki article: http://en.wikipedia.org/wiki/Shorin-Ryu
As well, check out this video of me demonstrating Fukyugata Ichi Kata for my fellow classmates.