Tai chi chuan (Traditional Chinese: 太極拳; Simplified Chinese: 太极拳; Hanyu Pinyin: tàijíquán; Wade-Giles: t'ai.

Overview
See also: History of Chinese Martial Arts
There are five major styles of tai chi chuan, each named after the Chinese family from which it originated:
The order of verifiable age is as listed above. The order of popularity (in terms of number of practitioners) is Yang, Wu, Chen, Sun, and Wu/Hao. The philosophical and political landscape of that time in Chinese history is fairly well documented. Tai chi's theories and practice are therefore believed by some schools to have been formulated by the Taoist monk Zhang Sanfeng in the 12th century, at about the same time that the principles of the Neo-Confucian school were making themselves felt in Chinese intellectual life. Zhang Sanfeng as a young man studied Tao Yin (導引, Pinyin dǎoyǐn) breathing exercises from his Taoist teachers and martial arts at the Buddhist Shaolin monastery, eventually combining the martial forms and breathing exercises to formulate the soft or internal principles we associate with tai chi chuan and related martial arts. Zhang Sanfeng is also sometimes attributed with the creation of the original 13 Movements of Tai Chi Chuan. These 13 movements are in all forms of tai chi chuan. Its subsequent fame attributed to his teaching, Wu Tang monastery was known thereafter as an important martial center for many centuries, its many styles of internal kung fu preserved and refined at various Taoist temples.

Chen style (陳氏)
Yang style (楊氏)
Wu or Wu/Hao style of Wu Yu-hsiang (Wu Yuxiang) (武氏)
Wu style of Wu Ch'uan-yü (Wu Quanyuo) and Wu Chien-ch'uan (Wu Jianquan) (吳氏)
Sun style (孫氏) History and styles
This family tree is not comprehensive.

Family tree
Names denoted by an asterisk are legendary or semi-legendary figures in the lineage, which means their involvement in the lineage, while accepted by most of the major schools, isn't independently verifiable from known historical records.
The Cheng Man-ch'ing and Chinese Sports Commission short forms are derived from Yang family forms, but neither are recognized as Yang family tai chi chuan by standard-bearing Yang family teachers. The Chen, Yang and Wu families are now promoting their own shortened demonstration forms for competitive purposes.

Notes to Family tree table
As the name tai chi chuan is held to be derived from the Taiji symbol (taijitu or t'ai chi t'u, 太極圖), commonly known in the West as the "yin-yang" diagram, tai chi chuan is therefore said in literature preserved in its oldest schools to be a study of yin (receptive) and yang (active) principles, using terminology found in the Chinese classics, especially the Book of Changes and the Tao Te Ching.
The core training involves two primary features: the first being the solo form (ch'üan or quán, 拳), a slow sequence of movements which emphasize a straight spine, abdominal breathing and a natural range of motion; the second being different styles of pushing hands (tui shou, 推手) for training movement principles of the form in a more practical way.
The solo form should take the students through a complete, natural, range of motion over their center of gravity. Accurate, repeated practice of the solo routine is said to retrain posture, encourage circulation throughout the students' bodies, maintain flexibility through their joints and further familiarize students with the martial application sequences implied by the forms. The major traditional styles of tai chi have forms which differ somewhat cosmetically, but there are also many obvious similarities which point to their common origin. The solo forms, empty-hand and weapon, are catalogs of movements that are practiced individually in pushing hands and martial application scenarios to prepare students for self-defense training. In most traditional schools different variations of the solo forms can be practiced: fast–slow, small circle–large circle, square–round (which are different expressions of leverage through the joints), low sitting/high sitting (the degree to which weight-bearing knees are kept bent throughout the form), for example.
The philosophy of the style is that if one uses hardness to resist violent force, then both sides are certain to be injured at least to some degree. Such injury, according to tai chi theory, is a natural consequence of meeting brute force with brute force. The collision of two like forces, yang with yang, is known as "double-weighted" in tai chi terminology. Instead, students are taught not to directly fight or resist an incoming force, but to meet it in softness and "stick" to it, following its motion while remaining in physical contact until the incoming force of attack exhausts itself or can be safely redirected, the result of meeting yang with yin. Done correctly, achieving this yin/yang or yang/yin balance in combat (and, by extension, other areas of one's life) is known as being "single-weighted" and is a primary goal of tai chi chuan training. Lao Tzu provided the archetype for this in the Tao Te Ching when he wrote, "The soft and the pliable will defeat the hard and strong."
Tai chi's martial aspect relies on sensitivity to the opponent's movements and center of gravity dictating appropriate responses. Effectively affecting or "capturing" the opponent's center of gravity immediately upon contact is trained as the primary goal of the martial tai chi student. The sensitivity needed to capture the center is acquired over thousands of hours of first yin (slow, repetitive, meditative, low impact) and then later adding yang ("realistic," active, fast, high impact) martial training; forms, pushing hands and sparring. Tai chi trains in three basic ranges, close, medium and long, and then everything in between. Pushes and open hand strikes are more common than punches, and kicks are usually to the legs and lower torso, never higher than the hip depending on style. The fingers, fists, palms, sides of the hands, wrists, forearms, elbows, shoulders, back, hips, knees and feet are commonly used to strike, with strikes to the eyes, throat, heart, groin and other acupressure points trained by advanced students. Joint traps, locks and breaks (chin na) are also used. Most tai chi teachers expect their students to thoroughly learn defensive or neutralizing skills first, and a student will have to demonstrate proficiency with them before offensive skills will be extensively trained. There is also an emphasis in the traditional schools that one is expected to show wu te (武德), martial virtue or heroism, to protect the defenseless and show mercy to one's opponents.
Other training exercises include:

Kung fu
Wushu
San Soo
Shaolin Temple
Wudang Mountains
Bodhidharma
Dong Haichuan
Huo Yuanjia
Wong Fei Hung
Wu Ch'uan-yu
Yang Lu-ch'an
Hong Kong action cinema
Wushu (sport)
Wuxia
Weapons training and fencing applications employing the straight sword known as the jian or chien or gim (jiàn 劍), a heavier curved sabre, sometimes called a broadsword or tao (dāo 刀, which is actually considered a big knife), folding fan also called san, wooden staff (2 m) known as kun (棍), 7 foot (2 m) spear and 13 foot (4 m) lance (both called qiāng 槍). More exotic weapons still used by some traditional styles are the large Dadao or Ta Tao (大刀) and Pudao or P'u Tao (撲刀) sabres, halberd (jǐ 戟), cane, rope-dart, three sectional staff, Wind and fire wheels, lasso, whip, chain whip and steel whip.
Two-person tournament sparring (as part of push hands competitions and/or sanshou 散手);
Breathing exercises; nei kung (內功 nèigōng) or, more commonly, ch'i kung (氣功 qìgōng) to develop ch'i (氣 qì) or "breath energy" in coordination with physical movement and post standing or combinations of the two. These were formerly taught only to disciples as a separate, complementary training system. In the last 50 years they have become more well known to the general public. Training and techniques
Tai chi has become very popular in the last twenty years or so, as the baby boomers age and the art's reputation for ameliorating the effects of aging becomes more well-known..

Tai chi as sport
Before tai chi's introduction to Western students, the health benefits of tai chi chuan were largely explained through the lens of traditional Chinese medicine; which is based on a view of the body and healing mechanisms not always studied or supported by modern science. Today, some prominent tai chi teachers have advocated subjecting tai chi to rigorous scientific studies to gain acceptance in the West.

Tai chi chuan in fiction



List of Tai Chi Chuan forms
World Tai Chi and Qigong Day
Li style T'ai Chi Ch'uan
Wudang Tai Chi Chuan
Tchoung Ta-chen
Taoist Tai Chi
Liuhe Bafa