SHOTOKAN KATA
The explanations are listed in this original thread from 2009
shirotoratiger.proboards.com/thread/57/karate-katas-explanation
The list:
Taikyoku shodan (太極初段), as discussed initially taught as Kihon No Kata
The 26 Core Shotokan Kata:
Heian shodan (平安初段),
Heian nidan (平安二段),
Heian sandan (平安三段),
Heian yondan (平安四段),
Heian godan (平安五段),
Tekki shodan (鉄騎初段),
Bassai dai (披塞大),
Kanku dai (観空大),
Enpi (燕飛),
Hangetsu (半月),
Jion (慈恩),
Jitte (十手),
Ji'in (慈陰)
Tekki nidan (鉄騎二段),
Tekki sandan (鉄騎三段),
Bassai shō (披塞小),
Kankū shō (観空小),
Chinte (珍手),
Unsu (雲手),
Sōchin (壯鎭),
Wankan (王冠),
Gankaku (岩鶴),
Meikyō/Rōhai (明鏡),
Gojūshiho shō (五十四歩小),
Gojūshiho dai (五十四歩大),
Nijūshiho (二十四步),
Some Shotokan Shihan practice and teach Seienchin
Some Shihan teach all 3 Taikyoku
These additional 4 would make a full list of 30 kata, as noted on the STMA Kata Thread
