This is the Wudang Zhang San-feng Tai Chi Chuan 13 form performed by master Chen Shi-Yu from Wudang Taoist Martial Arts School. It is believed that the Zhang San-feng form is the earliest Tai Chi form, named after its creator (Zhang San-feng).
The video is taken with permission from the following websites:
Wudang Zhang San-feng Tai Chi Chuan is also known as Wudang San Feng 13 form. Tai Chi is also known as Tai Ji Quan.