In 1889, the world is on the pinnacle of great discoveries in technology. In mankind's grasp for the future, a sinister foe known only as Gargoyle, obsessed with restoring the former Atlantean empire to the glory it once held, begins his plans to take over the world. Nadia, with the help of a young inventor, Jean Raltique, and the mysterious captain Nemo of the submarine Nautilus, must fight to save the world from Gargoyle and Neo-Atlantis. Based on the Novel '20,000 Leagues Under the Sea' by Jules Verne. 
(Source: Anime News Network)

Three years after the defeat of Gargoyle and Neo-Atlantis, a new threat has surfaced bent on bringing the world under his control. Geiger, using advanced robot technology, is attempting to begin a world war, and take control of the devistated world after the destruction has stopped. Once again, Nadia and Jean must fight to save the world, only this time from itself.
 
(Source: Anime News Network)

These short Omake "extra" episodes were included as a bonus on the Japanese LD set.

A shorter, more streamlined version of Nadia called "The Nautilus Story", which all but eliminates the filler arc and concentrates on the struggle between Nemo and Gargoyle. Some scenes in the more pivotal episodes are cut as well. The compilation series was made by Hideaki Anno, who was said to have been dissatisfied with the final result of the TV show. The Nautilus Story was only released in Japan on VHS and laserdisc.
 
(Source: TV Tropes, edited)

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