I feel a little mean for not liking this more.
I liked the general mood of derring-do, and I liked the two principal characters (especially after they met and started interacting directly). There are some fun set pieces (many of which feel like they would translate well to film).
But I found the relationship of world-building to narrative a bit frustrating. A bunch of the magical system is worked out with some rigor – there are rules about who can open doors between or within worlds, and how such doors can be opened. And then there’s also a theme of manipulating the traditional greek elements. In battles, wizardy types throw air, water, fire, etc. at each other; fine. But beyond that, there’s a whole bunch of other magic that doesn’t have the rigidity of the door rules, but also doesn’t have an elemental underpinning. We learn about one of these in the very first paragraph, a magic coat that can be turned inside-out multiple times with many somewhat non-deterministic results.
Maybe this will be the subject of later books in the series, but here the effect of this is that it wasn’t clear to me what was or wasn’t possible at any given point. That undercut the narrative stakes for me, because it always seemed possible for the characters to just use a new type of spell to overcome a particular plot obstacle. (Certainly not unique to this book; that bothered about Harry Potter too, so take my criticisms with the necessary quantity of NaCl).
Beyond that, I thought many of the characters slotted a little too neatly into familiar tropes, (especially the villains).
For the first volume of a trilogy, I thought this wrapped up quite solidly (although I also thought the protags made a really questionable decision that I assume leads to trouble in book two).
Rep note: One of the supporting protagonists is identified as bisexual.