The caving activites in Iceland are rather young, the Icelandic Speleological Society (ISS) was founded in 1989.
The first time, caving in iceland was described in literature is nevertheless much earlier: in the book A Journey to the Center of the Earth (1864), Jules Verne (*1828-✝1905) described how a scientific expedition into the earth entered the caves through an Icelandic volcano. From both the geologic and the speleological view, the book is pretty bad, but it is exciting entertainment.