I would like it to be finished as well.

Murasakiiro no Qualia is a great manga in this category and one of my favourites. It takes time travel very serious, presenting time paradoxes, the thought experiment of Schrödinger and quantum physics. The plot is very interesting and there is a big character development, especially the bond between the two main characters. the feels are coming back TT.TT
The sad part is that it is still ongoing, but it deserves a try.

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First - You can check the category Time Travel of the tag, which comes up with 12 pages full of time travelling recommendations and could be checked for finished stories with a specific search inquiry, matching your tastes. And coming to this - Do you prefer any specific genre, which could help to find the right kind of story? ^^

As for my personal recommendations on this, there are:

* Heptagon: A Josei story, which has a psychological touch and invovles a apathetic 24-year-old, that gets back to her 14-year-old junior high self and starts to remember bits of her past, that leads to her current state. It's a little dragging, but a thing to kill some time nicely with.

* Shinobi Life starts like a stereotypical Shoujo Manga, but with the plot developing it actually becomes a worthy (nice drawn) read, even showing off some unexpected twists and (historical) daily life issues.

* Tonari no Shugoshin is a typical Shoujo, yet brings in a fantasy build up, including time travel. Well, it's predictable, but is drawn in a way, that will satisfy the readers and can be worth a try.

* If you don't mind Yaoi, then Nemureru Tsuki and ≠ - Not Equal have both a psychological mystery feel and some really well-off drawing styles to offer. They are somewhat heavy tensed, nothing to go over speedily and take lightly, but that's what got them on my list. They are something to think over, the first even involving some classical thriller and crime elements.

* Zettai Kareshi is a classical in the Shoujo romance genre. If I'm not mistaken, then one of the oneshots added has a time travel plot ... Not sure tho. Sry.

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"It's like love is a bonus in your life. Even without it, I'm just fine. I don't feel like pointlessly searching for it. You don't have to make yourself unhappy." (Ookami Shoujo to Kuro Ouji)

"Why does it rain?" - "To create drama." (Drops (Andou Yuki))