Taoist Zhang San Feng
There is a legend that suggests that the well known Taoist Zhang San Feng created the concept of Tai Chi in the 13th century. He is said to have lived between 1279 and 1368.When he was just 5 years old, he suffered from an eye disease. He was fortunate to be healed by a Taoist named Zhang Yunum. Zhang Sanfeng is the sixth generation descendant of the Laozi-founded Yinxian Sect.
Snake / Crane Combat
He spent time at the Purple Summit Temple on Wudang Mountain in China when he came across a crane and a snake in combat. He observed a bird attacking a snake and was greatly inspired by the snake's defensive tactics. It remained still and alert in the face of the bird's onslaught until it made a lunge and fatally bit its attacker. It was this relationship of energy between opponents and the self-defense style (evasive action, yielding, and attacking) that inspired Zhang to create Tai Chi Chuan, which is what we now know as Tai Chi.
Zhang San Feng created the 13 classic Tai Chi postures, which are believed to be the first documented Tai Chi movements. After that Wang Tsung-Yueh refined the 13 classic Tai Chi movements.
Different Tai Chi Styles
Chen Wang-ting used the refined 13 classic Tai Chi movements as the foundation for his newly created family style of Tai Chi, which was improved/influenced by his military and boxing knowledge. Chen style is the oldest Tai Chi style which was the foundation for all the other upcoming Tai Chi styles.
For more details for the different Tai Chi style please refer to the Tai Chi styles article