Series is not complete yet. So my review will be edited later.
So far the draw here seems to be the development of romance between the son Gwi-ju (Gwi-joo) who can travel backward in time and the "adopted" maid Da-hae who comes from a gang of crooks. Initially the son is disinterested, and the maid is conniving to scam his rich family. But as things evolve it is clear they are interested in each other and more is at stake.
The time traveling son seems confused about what he can do as a time traveler. When he goes back to revisit a past event he can move about and learn details surrounding that moment in time, a bit like a news reporter could wander and talk and see things not known by participants when the event originally occurred. That can cast light upon what actually happened and upon motivations of those involved, and those details can inform the present when the son returns to his time. There is some tension whether this added information might conflict with what the people in the present want to portray as what happened. So Gwi-ju can bring info from the past to the present that then will change the future from what would happen if that info were not made available.
But things from there become confused: can the son actually meddle with the past itself when he's back there in a way that changes the present moment? For a while he doubts that. But apparently he can.
For example, in Episode 8, Da-hae and Gwi-ju sit on a bench with gang member Hyeong-tae, who is acting as a chaperone. Wanting to ditch the chaperone, Gwi-ju persuades Hyeong-tae to come with him and leave Da-hae sitting on the bench. The two guys then go on a long train trip and at the last train stop, Gwi-ju dematerializes, ditching Hyeong -tae, and traveling magically back in time to Da-hae still sitting on the bench and still at the same time as when he left her earlier. He then hands her the winning lottery numbers he happened to see in the present at the final train station, and tells her to buy a ticket now with those numbers to make money. And then Gwi-ju returns to the present at the train station and picks up the bewildered Hyeong-tae.
So we see that Gwi-ju can go back in time with information from the present, and make folks rich by giving them that knowledge about the yet to arrive present. Now informed about what is coming, they then can act at that earlier time so as to benefit themselves when the present actually arrives. Clearly altering the past and producing a different future. Confusing enough?
Various machinations between the son's family and the maid's con artist pals serve to keep the two lovers in turmoil. Needed to make the course of true love not run smooth.
By and large the story is engaging. The actors do well. But the capabilities of backward time travel needs to be straightened out. Will the crooks become good guys? Will the daughter's ability to fly actually turn out to be useful? Will the mother finally get what's going on? Guess things will work out.