Translations are approximate transliterations of the Chinese characters used to "spell" the kata names.
• kata -- form(s)
• heian shodan -- "stable and secure / stable peace, first level"
• heian nidan -- ditto, "second level"
• heian sandan -- ditto, "third level"
• heian yondan -- you get the idea
• heian godan
• tekki shodan -- "iron horseman," "first level"
• tekki nidan
• tekki sandan
• bassai dai -- "destroying a fortress, greater (version)" (*)
• bassai sho [shoh] -- "destroying a fortress, lesser (version)" (*)
• empi -- "flight of the swallow"
• jion -- "compassion and favor." This is a Buddhist term and possibly the name of some temple.
• kankuu dai -- "observing the sky/emptiness, greater (version)" (*)
• kankuu sho [shoh] -- "observing the sky/emptiness, lesser (version)"(*)
• jutte / jitte -- "ten hands"
• hangetsu -- "half-moon"
• nijuushiho -- "twenty-four steps"
• gankaku -- "boulder crane" (the bird on a rock)
• sochin [ soh-chin] -- "strength and control"
• unsu [unsuu] -- "cloud hands"
• gojuushiho ( dai) -- "fifty-four steps, greater (version)" (*)
• gojuushiho sho [shoh] -- "fifty-four steps, lesser (version)" (*)
• meikyo [ meikyoh] -- "bright mirror"
• ji'in -- "compassion and shadow." Possibly another temple.
• chinte -- "rare hands"
• wankan -- "king's crown"
(*) Kata with "lesser" or "greater" attached ("sho" or "dai") don't really mean "lesser" or "greater" in any sense. It's just a way of distinguishing two different kata.