In the International Taekwon-do Federation, there are 24 Tul (patterns). Originating under a foreign influence, they have been improved, updated and modernized to suit the requirements of contemporary living. The originator, General Choi, Hong Hi, (Deceased) chose the number 24 intentionally to create, symbolically, one form for each hour of the day. One who is truly in Taekwon-do, lives by its tenets 24 hours a day. (I have included Ko Dang Hyung for the old ITF players even though Ju Che has replaced it in modern ITF TKD)
In the World TaeKwonDo Federation, there are 25 forms. There are eight (8) Tae Geuk, eight (8) Pal Gwe and nine (9) black belt Poomse (patterns). The black belt patterns are supposedly dedicated to each of the nine (9) Kwans (schools), from which the W.T.F. consists of.

White Sa-Ju Chiruki (ITF) 17 Four (4) Directional Punch
  Ki-Cho Il-Bu, Ee-Bu, Sam-Bu (WTF) 20 each Basic Form 1, 2, 3
White with Yellow stripe Chon-Ji (ITF)  19 Heaven and Earth
 Pal Gwe Il Jang (#1) (WTF) 20 1st Set of 8 Trigrams (3 bars) Pal=8 and Gwe=Trigram
 Tae Geuk Il Jang (#1) (WTF) 20 Great universe 1st form (Tae Geuk also means Korean flag)

Yellow Dan Gun (ITF) 21 Holy Dan Gun, founder of Korea in 2333 B.C.
Pal Gwe E Jang (#2) (WTF) 26 2nd Set of 8 Trigrams (Taken from the I Ching, "Book of Changes")
Tae Geuk E Jang (#2) 23 Great universe 2nd form

Yellow with Green stripe Do San (ITF) 24 Pseudonym of Ahn Chang Ho, freedom fighter and educator 1876-1938
Pal Gwe Sam Jang (#3) (WTF) 22 3rd Set of 8 Trigrams 
Tae Geuk Sam Jang (#3) (WTF) 34 Great universe 3rd form

Green Won Hyo (ITF) 28 Monk who introduced Buddhism to Korea in 686 AD
Pal Gwe Sah Jang (#4) (WTF) 28 4th  Set of 8 Trigrams 
Tae Geuk Sah Jang (#4) (WTF) 28 Great universe 4th form

Green with Blue stripe Yul Gok (ITF) 38 Pseudonym of Yi I, 1536 philosopher nicknamed "Confucius of Korea"
Pal Gwe Oh Jang (#5) (WTF) 39 5th  Set of 8 Trigrams 
Tae Geuk Oh Jang (#5) (WTF) 32 Great universe 5th form

Blue Joong Gun (ITF) 32 Joong Gun, patriot, freedom fighter, assassinated the first Japanese Ambassador in 1910. 32 movements is the age of Joong Gun when he was executed.
Pal Gwe Yuk Jang (#6) (WTF) 29 6th  Set of 8 Trigrams 
Tae Geuk Yuk Jang (#6) (WTF) 28 Great universe 6th form

Blue with Red stripe Toi Gye (ITF) 32 Pseudonym of Yi Hwang, 16th Century Neo-Confucian scholar.
Pal Gwe Chil Jang (#7) (WTF) 29 7th  Set of 8 Trigrams 
Tae Geuk Chil Jang (#7) (WTF) 32 Great universe 7th form

Red Hwa Rang (ITF) 29 Elite military group in Silla, 500 AD
Pal Gwe Pal Jang (#8) (WTF) 39 8th  Set of 8 Trigrams 
Tae Geuk Pal Jang (#8) (WTF) 39 Great universe 8th form

Red with Black stripe Chung Moo (ITF) 30 Admiral Yi Sun Sin, 1592, first "kobukson" (Iron Turtle Ship)
Koryo (WTF) 50 Kingdom of Korea (918-1392 AD) 

Black 1st Dan Kwang Gae (ITF) 39 Kwang Gae T'o was a king of Koguryo Dynasty. 39 moves depict years of reign.
Po Eun (ITF) 36 Pseudonym of Chong Mong Chu, poet, physicist in 1400 AD 
Gae Baek (ITF) 44 General in Pak Chae Dynasty 660 AD
Kum Gang (WTF) 27 Diamond, symbol of hardness and strength, wisdom and virtue. 

Black 2nd Dan Eui Am (ITF) 45 Pseudonym of Son Byong Hi, leader of the Korean independence movement in 1919.
Choong Jang (ITF) 51 Pseudonym of General Kim Duk Ryang, Joseon Dynasty in the 15th century. 
Ju Che (ITF) 45 Juche
Ko Dang (ITF) 39 Pseudonym of Cho Man Sik, patriot of independence movement. 39 moves signify his time of imprisonment.. 
Tae Baek (WTF) 40 Mountain range, (now Mount Baek Doo) 

Black 3rd Dan Sam Il (ITF) 33 33 Patriots independence movement, March 1, 1919
Yu Sin (ITF) 68 General Kim Yu Sin of Silla, who united the 3 kingdoms of Korea 
Choi Yong (ITF) 45 Koryo dynasty general executed for loyalty to king
Pyong Won (WTF) 33 Simple, plain and unpretentious. Also plains and valleys. 

Black 4th Dan and above Yong Gae (ITF) 49 General in the Korguryo dynasty who defeated the Chinese in 649 AD
Ul Ji (ITF) 42 General UlJi Mu Duk, who in 612 AD defended Korea against 1 million Chinese invaders 
Moon Mu (ITF) 61 King of the Silla dynasty in 661 AD. Fighter against  Japan.
Ji Tae (WTF) 37 Earth (everything comes from and goes back to Earth). 
  Sip Jin (WTF) 41 Decimal point, perfect numerical system

Black 5th Dan and above So San (ITF) 49 Pseudonym of Choi Hyung Ung, 1520-1604, Monk, Fighter against Japan
Cheon Kwon (WTF) 38 Sky, symbol of Heaven, Ruler of the universe and all human beings

Black 6th Dan and above Se Jong (ITF) 24 King, Inventor of Korean Alphabet (1443), 24 moves signify 24 letters in alphabet. 
Han Soo (WTF) 33 Water (forceful and life giving element), fluidity, strength and adaptability 

Black 7th Dan and above Tong Il (ITF) 56 Denotes the resolution to unify Korea, divided since 1945
Il Yo (WTF) 28 Oneness (ultimate unification with God and nature)

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Updated on FEBRUARY 12, 2014!