Sword of the Demon Hunter: Kijin Gentosho

In the Edo period, there was a shrine maiden called "Itsukihime" in the mountain village of Kadono. Jinta, a young man who acts as the shrine maiden's guardian despite being a stranger, encounters a mysterious demon who speaks of the far future in the forest where he went to defeat it. From Edo to the Heisei era, this huge Japanese fantasy series follows a demon man who travels through time while continuously questioning the meaning of wielding a sword.

(Source: Crunchyroll, edited)