Nadia Omake Gekijou

Nadia Omake Gekijou (English: Nadia's Omake Theater) is a collection of ten animated featurettes humorously explaining and expanding the universe of Nadia: The Secret of Blue Water. These were created by Studio Gainax who had created the original series and released initially on LaserDisc and later on DVD. Release date was very close to the time NHK was airing the series. Categorically, they constitute, as the title clearly suggests, Omake to the series.

Directors involved were: Hideaki Anno, Hayao Miyazaki, Takeshi Mori, Kazuya Tsurumaki, among others.

Titles and Synopses of the Featurettes

(WARNING: POTENTIAL SPOILERS AHEAD)

1889: Nadia's World - about Paris, Eiffel Tower in particular, as of 1889 with added fictional details. "Introduces" Jules Verne.
This is Neo-Atlantis - black-and-white animation styled after WWII German propaganda films with Gargoyle making a speech suspiciously similar to Adolf Hitler's fervent speeches. Uses evocative symbols.
26 Secrets of the Invincible Submarine Nautilus - gives "technical" details and statistics on Nautilus. The actual number of secrets revealed is far less than 26 because, Elektra says, "they are s-ec-ret."
The Big Secret of Blue Water - nature and qualities of Blue Water are explained by Elektra to a rod puppet of Marie. Some humurous character dynamics.
Nadia Enters a Pageant (Out of 39) - designated in the title screen as "Episode 17.5" goes over the story of an almost "normal" day in Nautilus.
Welcome to Neo-Atlantis - Gargoyle plays a curator and introduces Neo-Atlantis and its army to the habitually irreverent and instinctively practical Marie. Hangs a lampshade on the unexplained destruction of Gargoyle's knock-off Tower of Babel.
Nadia Super Encyclopedia (This is Nadia! Nadia's Secret File) - goes as far as giving Nadia's measurements and "interviews" with her reluctant acquaintances. A photo of Hideaki Anno appears in a cutout animation near the end.
Sunset JanJan - designated (playfully) "Episode 52." Features Nadia and Jean in a form of Japanese talk show unknown to this troper showcasing their memorable moments through occasionally embarrassing photos.
In Search of that Lost Time - playing on the title of Marcel Proust's magnum opus, features a tipsy, moody Elektra at the (actual) Shige-chan bar in Ikebukuru, Tokyo giving some details about what happened to Nautilus' crew while Nadia, Jean, and Marie were on the desert island, i.e. during the Island arc. Her relationship to Nemo is confirmed.
Comparison! New Nautilus versus Red Noah - some more "technicalities" plus outright Lampshade Hanging to humorous effect.

Tropes used in Nadia Omake Gekijou include:

Alternate Universe: The Revision on Welcome to Neo-Atlantis (described below) tries to explain an event in one reality, destruction of Gargoyle's first Tower of Babel, in terms of interference from the comical parallel reality of the featurette.
Lampshade Hanging: Multiple times the featurettes allude to the weak points of the series' long and complex plot. The creators' "we-know-it-was-lame" nod.
Revision: During Welcome to Neo-Atlantis, Marie "accidentally" presses the self-destruct switch of Gargoyle's first Tower of Babel in effect explaining how the destruction happened in the first place.
Shout-Out: Obvious ones are to the series itself. Less obvious ones are to many works of literature, historical events, and scientific ideas.
The Un-Reveal: As mentioned above, 26 Secrets of the Invincible Submarine Nautilus reveals far fewer than 26 secrets.