Hey Nostyle,
I don't mean to be mean, but please ignore the comments before mine.
They are largely incorrect.
As FrankTheAnvil has correctly found out, this song is set in A minor
(Unfortunately, the chords are incorrect).
The intro starts out 100% A minor:
Am | F | Em | Am
But I guess your question was about what follows after that.
This song what's known as "modal interchange" once the vocals come in:
Am | B (V/V) - E (from harmonic minor)
Am | D (from Dorian)
F | D | F | D
It mostly repeats these chords after that.
Sound confusing? Let me know what's unclear and I'll shed some light.
Best,
Friedemann