It's easy enough to find a manga that does time travel. I find that most time travel stories are rather simple; they usually go into the past, change one or two little things, and then they get a more favorable outcome. Dragon Ball and Doraemon both have time travel, but they don't seem to worry too much about the fine details.

I would like to read a time travel series that is actually confusing to read. Something where even the slightest little thing causes a massive change in the future, maybe even deal with paradoxes and such. To make it really messy, maybe the protagonist changes something in the past, prevents the problem from occurring in the future, but something even worse happens, so he has to go back even further into the past to get to the root of the issue.

I would ideally prefer something where it sounds like the author has done his/her homework on the theory of time travel, so the story is a literary mess, but technically sound (or at least mostly).

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If I've made a thread in the "I'm Looking For..." forum, I am only interested in Japanese manga. I am not interested in non-Japanese media at this time.

Steins;Gate. Not very complicated but the trial and error they take makes it a lot more interesting than time travel as a sub-plot as you mentioned. Highly recommending the anime for this though.

Murasakiiro no Qualia probably fits the best that I know of.

Dreamcide is fun too, though the time travel is a lot more fantastical.