Adults have free dress, meaning you can wear what you're comfortable in (whether that is leotard and tights, or fitness wear). Ballet shoes are recommended, but not required. You could take your first class in socks, if you'd like to decide if you want to continue with the class/get ballet shoes.
If you're going to learn ballet, yes you need to wear proper ballet attire of course. You can always call or visit them if you have any further questions.
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