Who is the person who studies caves?

A speleologist is the scientific name, like Oceanographer. Amateur Cave explorers are called Cavers. The term is derived from Spelea- Latin- Cave.

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Many speleogists, whether amateur or professional scientists,call themselves simply "cavers" even if they use "speleology" to describe their studies. Apart from modesty you can't study a cave unless you are also a caver!