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Wudang quan is a class of Chinese martial arts.
In contemporary China, Chinese martial arts styles are generally classified into two major groups: Wudang (Wutang), named after the Wudang Mountains; and Shaolin, named after the Shaolin Monastery.  Wudang quan (Chinese: 武当拳; pinyin: Wǔdāng quán; Wade–Giles: Wu3-tang1 ch'üan2) translates as "Wudang fist." Whereas Shaolin includes many martial art styles, Wudangquan includes only a few arts that utilize the focused mind to control the waist, and therefore the body; this typically encompasses T'ai chi ch'uan, Xing-Yi chuan and Bagua zhang, but must also include Baji chuan and Wudang Sword.: Although the name Wudang simply distinguishes the skills, theories and applications of the internal arts from those of the Shaolin styles, it falsely suggests these arts originated at the Wudang Mountains. The name Wudang comes from a popular Chinese legend that incorrectly purports the genesis of Tai chi chuan and Wudang Sword by an immortal, Taoist hermit named Zhang Sanfeng who lived in the monasteries of Wudang Mountain.
The term neijia and the distinction between internal and external martial arts first appears in Huang Zongxi's 1669 Epitaph for Wang Zhengnan. Stanley Henning proposes that the Epitaph's identification of the internal martial arts with the Taoism indigenous to China and of the external martial arts with the foreign Buddhism of Shaolin—and the Manchu Qing Dynasty to which Huang Zongxi was opposed—was an act of political defiance rather than one of technical classification.
In 1676 Huang Zongxi's son, Huang Baijia, who learned martial arts from Wang Zhengnan, compiled the earliest extant manual of internal martial arts, the Neijia quanfa.
In the late 1800s, Dong Hai Chuan began teaching Bagua Zhang to a very select group of individuals. The highly-notable Xing-Yi stylist Liu De Kuan was among those who learned this special art from Dong. Liu was a very friendly martial artist who had also learned T'ai chi ch'uan from Yang Luchan. Liu's friendly nature and experience with the three "internal" martial arts created an easy forum for discussion and knowledge-sharing between practitioners of these arts.
In 1894, an alliance was created with Cheng Tinghua taking the lead and representing Bagua Zhang; Li Cun Yi and Liu Wei Xiang represented Xingyiquan; and although Liu De Kuan practiced all three arts, he represented T'ai chi ch'uan. The alliance grouped the three arts under the umbrella of "Neijia," and swore brotherhood among its associates and practitioners. Cheng Ting Hua was shot and killed by German soldiers during the Boxer Rebellion (1900), which likely strengthened the alliance.
Republic of China
Around 1912, the third-generation BaGua master Fu Chen Sung was traveling throughout Northern China to meet and learn from the best martial artists when he met Wudang Sword grandmaster Sung Wei-I in Liaoning Province; Fu learned Sung's Wudang Sword and fighting forms: Lightning Palm and Rocket Fist. Fu joined General Li Jinglin's army in 1920. General Li Jinglin had also met Sung Wei-Yi in the early 1900s while garrisoned in Lia Ning Province, and had also learned Sung's Wudang Sword techniques.
In 1925, General Zhang Zhi Jiang began to propagate his belief that martial arts should be used to improve the health of the Chinese people. He suggested the creation of a Central Martial Arts Academy (Central Guoshu Institute), and was named Director. General Li Jinglin, retired from his military career, was named Vice-Chairman to the Academy. General Li's kung fu advisor was the famous Bajiquan master Li Shuwen.
In 1928, Kuomintang generals Zhang Zi Jiang, Fung Zu Ziang and Li Jinglin organized two national martial arts tournaments in Beijing & Nanjing respectively; they did so to screen the best martial artists in order to begin populating the Central Martial Arts Academy. The generals separated the participants of the tournament into Shaolin and Wudang. Wudang participants were recognized as having "internal" skills. These participants were generally practitioners of T'ai Chi Ch'uan, Xingyiquan and Baguazhang. All other participants competed under the classification of Shaolin. Thus, Wudangquan came to encompass Tai Chi, Bagua, Xingyi; Baji from Li Shu Wen; and Wudang Sword from Sung Wei-I and Li Jing Lin. Fu Chen Sung won the fighting competition in Beijing, and was named head Bāguàzhǎng instructor for all of China.
Circumspectively, this seems to be the historical point when the name Wudang became the prevalent moniker for the internal martial arts across China.
The two major lineages of Wudang Chuan were passed down from Li Jinglin. These lineages went to Fu Chen Sung and Yang Kui-Shan.
Fu Style Wudang Quan
Fu Chen Sung (Fu ZhenSong) worked the rest of his life to develop Fu Style Wudang Fist. The system included exercises, empty hand and weapons sets in Tai Chi, BaGua, Hsing-Yi—and Fu Chen Sung's well-documented, signature forms: Liang-Yi Chuan, Dragon Palm BaGuaZhang and Dragon Palm BaGua Push hands (most of which he created in the 1940s); the famous but extremely rare Wudang Sword techniques were embodied in Fu's progression of Tai Chi Sword, to Seven Star Sword, to Bagua Cyclone Broadsword, and finally, Flying Dragon Bagua Sword forms. In his lifetime, Fu had many notable students, including General Sun Pao Gung and Lin Chao Zhen. Fu's oldest son, Fu Wing Fay (Fu Yong Hui), became Fu's prodigal son. Wing Fay grew up among many of the greatest martial artists in the Golden Era of Martial Arts in China. Wing Fay learned well from his father and the other great masters. Wing Fay practiced hard, and began developing Fu Style Wudang Fist even more. Wing Fay had two top students: his son, (Victor) Fu Sheng Long, and Bow Sim Mark (the mother of Donnie Yen).
Wudang Dan Pai
According to T'ai Chi Magazine, volume 29, no. 3, Wudang Dan Pai claims direct descent of Zhang SanFeng. Starting in the Ming Dynasty with Zhang Song-Xi, Wudang Dan Pai has been passed down for 13 generations. Its 9th generation lineage holder was Sung Wei-I, who was the first non-Taoist to hold the lineage. Sung passed the lineage to Li Jinglin (for the 10th). Li passed the lineage to Yang Kui-Shang (for the 11th), who passed it on to Qian Timing (for the 12th).  The 12th generation headmaster and Gatekeeper of Wudang Dan Pai in China was Ma Jie, who learned his techniques from Daoist master Xuan Dan, Wudang Sword master Meng Xiao-Feng, and Xingyiquan and Baguazhang master Han Mu-Xia. Ma Jie's closed door disciples, Chang Wu-Na and Lu Mei-hui (who are also disciples of Qian Timing) are the current masters and gatekeepers of the 13th generation.:xiii-xiv
At the time Li Jinglin held the lineage, Li and his contingent were learning BaGuaZhang from Fu Zhen Song; XingYi Quan from Sun Lu Tang; Tai Chi Chuan from Yang ChengFu; Baji Quan from Li Shuwen; and the Wudang Sword techniques had come from Sung Wei-I.
Techniques include: Wudang Sword (6 sections 132 movements), Wudang Qigong Taijiquan, Wudang Neigong Taijiquan, Wudang Two-Man Sword Dueling Forms, Wudang Flying Sword, Xingyiquan, Baguazhang, Dian Xue Point Striking, Taiji Push Hands, Wudang Sword Sparring, Taoist Nei Dan Gong, and other meditation practices. The push hands features a combination of Chinese Wrestling and joint locking.
The system is known for its emphasis on practical applications, and its fighting and healing abilities, with many of its masters entering full contact competitions or becoming traditional healers. Equal emphasis is placed on internal training and external strength.
Wudang Taiyi Boxing
According to T'ai Chi Magazine, volume 30, no. 1, Yang Qunli claims Jin Zitao started learning Wudang Taiyi Wuxing Boxing from Li Heling at Wudang Mountain in 1929. The article connotes that from the time of Li's death until the early 1980s, Jin Zitao was the only person alive who had knowledge of the secret martial arts of Wudang Mountain. In 1980, Jin Zitao demonstrated Wudang Taiyi Wuxing Boxing to the National Wushu Viewing and Emulating and Communicating Congress in Taiyuan City, Shanxi Province. Before that, it had "never been shown before."
The article cites Jin's association with "The Institute of Wudang Boxing" and the "Journal of Wudang." 
According to Kung Fu Tai Chi Magazine, Zhong Yun Long went to Wudang Mountain in 1984, and studied under the 13th generation masters, Guo Gaoyi and Wang Kuangde. Zhong became the 14th generation lineage holder of the Wudang SanFeng Sect. The article cites their association with the 'Wudang Taoist Association."
There does not seem to be any connection between Jin Zitao and the Wudang San Feng Sect except for the fact that they both use the term "Taiyi" as the name of a form. Both lineages claim to be direct descendants of Zhang San Feng, and claim they learned Wudang martial arts at Wudang Mountain in the 20th century.
Currently, a contingent of Taoist martial art masters claiming lineage to Zhong Yun Long practice and teach Wudang martial arts at Wudang Mountain, which was named a World Heritage Site by the United Nations Educational Scientific Cultural Organization in 1994. These Taoists practice what they call Wudang Wushu or Wudang GongFu, and worship Zhang SanFeng as a deity. The website shows a curriculum of Tai Chi, XingYi, BaGua, QiGong, meditation and LiangYi (Tai Yi Wu Xing Quan), and claims BaGuaZhang originated there. These masters and the Fu Family are the only two schools that teach a martial art form called LiangYi.
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