If you liked
Full Metal Panic!
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...then you might like
Suisei no Gargantia
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Similarities: - Mecha - Both involve a single soldier experiencing a different life - Both soldiers have no clue about the world around them - They also both don't know anything besides how to fight - They both involve a female protagonist Differences: - Redo comes from a different world all together - This has a more discovery/adventurous feel while FMP! has a comedy feel.
If you liked
Samurai Champloo
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...then you might like
Brave 10
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They're both similar in terms of coincidental meetings between male and female in the samurai era where the male has to protect the female even though he doesn't really want to, except Samurai Champloo has 2 males and 1 female and is more realistic to the era where as Brave 10 has a mix of several powers and more colour.
If you liked
K-On!
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...then you might like
Yuru Yuri
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Yuru Yuri is like K-ON! just without the music genre. Both are about a group of girls and both have a "tea" theme going on. Even the characters have similarities with K-ON! characters.
If you liked
Ikoku Meiro no Croisée The Animation
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...then you might like
Usagi Drop
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Though different art styles and different time era's, both consist of a male looking after a little girl and you get to witness the events that happen when the two lives collide.