Tenchi Muyo is one of the most convoluted titles because there are many different 'versions' of it. The various universes that bare the Tenchi title or use the Tenchi Muyo characters do not necessarily connect to each other the way they would seem to, or don't connect at all. Here are the Tenchi continuities that are available and where they go in relation to each other.
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Tenchi Muyo! [Ryo-Ohki] 1
Tenchi Muyo! [Ryo-Ohki] 2
Tenchi Muyo! [Ryo-Ohki] 3
Tenchi Muyo! GXP
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This is the original continuity, Tenchi Muyo! [Ryo-Ohki] 1 being the first Tenchi show to be produced. GXP is an official OAV spin off series based around the Galaxy Police.
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Tenchi Muyo: Mihoshi Special
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The full title is Galaxy Police Mihoshi's Space Adventure. This single OAV is generally considered part of the Tenchi
Muyo! [Ryo-Ohki] series and was the first time Kiyone featured in an episode, as did Pretty Sammy. I have listed it
as a separate continuity because the creator of Tenchi Muyo! [Ryo-Ohki] has said the Kiyone is not a part of that
continuity and will not feature in it in the third OAV series.
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Tenchi Muyo! [Ryo-Ohki] 1
No Need for Tenchi (manga)
The All New Tenchi Muyo! (manga)
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The No Need for Tenchi manga continues events from the end of the first OAV season and takes it off on a different angle.
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Tenchi Universe
Tenchi The Movie: Tenchi Muyo in Love
Tenchi Muyo in Love 2: Tenchi Forever
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This is the first alternate Tenchi continuity. The Tenchi Universe TV series retells the story in a completely different
way. The only firm connection between this and the Tenchi Muyo! [Ryo-Ohki] series is that the cast is the same, with
the addition of Kiyone to the 'family'. Some people do not like the Tenchi Forever movie due to it's more mature and
serious nature, so choose not to count it as part of this continuity.
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Tenchi in Tokyo
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This second TV series is not directly connected to the first, although some people will say it takes place after the Tenchi
Universe series, despite the inconsistencies.
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Tenchi Muyo: Manatsu no Eve (Daughter of Darkness)
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This film is considered by many to be a part of the Tenchi Muyo! [Ryo-Ohki] series some time after Kiyone joins
the cast. It is in fact a stand alone movie based on a set of Japanese Tenchi Muyo novels. It's original title translates to
'Tenchi Muyo: Midsummer's Eve' but was, for some reason, released as Tenchi Muyo The Movie 2: Daughter of Darkness, despite
the fact it does not follow on from the first movie.
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Magical Girl Pretty Sammy
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This is a Tenchi Muyo spin off OAV series, not connected to the other series' in any way exept the cast. Sasami takes part
as the star of this magical girl show, which also spoofs the genre.
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Magical Project S
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Just like Tenchi Universe did with Tenchi muyo! [Ryo-Ohki] , this is a complete retelling of Magical Girl Pretty Sammy in full TV series format.
All in all I recommend starting with the Tenchi Muyo! [Ryo-Ohki] series. It is the definitive Tenchi Muyo and generally considered to be the best of the lot outside the movies. Then go for the Tenchi Universe series and the three movies. If you still want more after that go for the Mihoshi Special, No Need for Tenchi manga and Tenchi in Tokyo. The Pretty Sammy spin offs can be seen whenever you like since they work just as stand alone series', although you might want to see some Tenchi to help get a few of the gags and an introduction to the characters in their normal setting. I also recommend seeing the OAV series before Magical Project S as Magical Project S has several gags for viewers who have seen the Pretty Sammy OAV series and you will be able to gauge if it is to your taste, although I actually find Magical Project S funnier.