Jin (Japanese) - two seasons, but the story is continuous. I haven't seen the Korean remake, can recommend the original. A brain surgeon finds himself back in time in the Edo period.
Is "being transfered into game with historical setting" also considered as time travel? If yes, then: My Queen - FL is transfered from a modern time to a game world, where she becomes princess and sets out on a funny adventure to find her true love. :)
Korean crime thriller Tunnel - loved the main lead and though it's set up like a crime thriller, it is also a time travel of sorts. Chinese fantasy Lost Love in times - loved the political intrigue and the various princes surrounding the FL.
