There is a *lot* of terminology in gymnastics. I couldn't possibly list it all. I suggest Googling a gymnastics dictionary.
What do you mean by basic skills? Basic skill for pre-competitive? Level 4? Level 8? Level 10?
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there are a ton of different moves in gymnastics. its almost impossible to name them all. the different apparatus are beam vault floor and bars. there are different moves depending on your level. for example: if you were in level 1 you would be doing forwards and backwards rolls, cartweels, and handtands on floor. if you were in level 2, you would be doing backbends roundoffs and handstand bridges on floor. but as you level up the moves/skills get much harder on every apparatus.
There are way too many gymnastics terms to simply be able to list them here for you. I suggest Googling a gymnastics dictionary.