The origins or Tai-Chi are lost in midst's of time. There are many legends of where it comes from, however trying to unpick the truth out of the tapestry myths and wild exaggerations common to Chinese martial history is all but impossible.
What is known however is that almost all modern forms of Tai-Chi have their roots in a fighting art or Wu Shu (We in the West commonly use the term Kung-Fu, which is in fact a general Chinese term that simply translated means 'a skill gained by hard work' and is not solely used to describe martial arts) developed in the 17th century by the Chen family in a village in Henan Province of China just North of the Yellow river.
This art, which had yet to adopt the name Tai-Chi was kept within the family until the late 18th century when it was passed on to Yang Luchan, Yang came from a poor family and was taken in by the Chen Family at the age of nine. There are various myths around how he became the first outsider to learn this family art, most involve him observing the family practice in secret until caught practising himself, at which point he is adopted as a student because of his obvious skill (this sort of story, along with gaining techniques from dreams, is common among the founders of many Chinese martial arts styles).
Whatever the actual truth, Yang Luchan was taught the family style and on the death of his master released from service. He returned to his home village of Yongnian and then from there, by introduction from a wealthy family he had befriended, to Beijing. It was here Yang Luchan began to teach more widely and began to modify what he had been taught to make it more appealing to a wider audience, it was also probably Yang that christened the art Tai Chi Chaun or Taijiquan (depending of the anglisation, Chaun or Quan means 'Fist' and is a commonly used term to denote a martial art, So Tai Chi Chuan roughly means Supreme Ultimate Fist).
Yang Luchan passed the art on to his sons who then passed it down to the next generation, the next figure to loom large in Tai-Chi history is Yang ChengFu (in more ways than one, as by the time of his Death Yang was not a small man). He is accredited with really starting to popularise Tai-Chi, not just as a Martial art but as a Health giving exercise. He also produced some of the first written literature on Tai Chi (or at least lent his name to, as Yang Chengfu was widely known to be illiterate so his work was ghost written by his more scholarly students).
Of Yang Chenfu's students the one that concerns us most is Cheng Man-Ch'ing (because in my classes this is the style I teach), already an accomplished painter and teacher he took up Tai-Chi because of a serious lung complaint and became one of Yang Chengfu's senior students (Ghost writing his second book, The Substance and Application of T'ai Chi Ch'uan). He is often referred to as 'The Master of the 5 excellences' because he was considered an authority on the traditional skills of a Confucian scholar (Medicine, Martial Arts, calligraphy, painting and poetry). He taught Tai-Chi in Taiwan and the brought it to America where he became one of the first people to teach Tai-Chi openly to non-Chinese. He also altered Yang Chengfu's form slightly, reducing the number of moves by removing some of the repititions and applying some stylist differences developed from his own training.