Karl Johnson's The Loki Variations digs into the character of Loki -- not specifically the Norse god in his original form, nor Loki just as portrayed by Tom Hiddleston, but Loki as an overall concept. Pretty much what it says on the tin, in fact: he's looking at the varied ways people have portrayed and enjoyed Loki's character, and what he's meant to people. 

It's nice to read something that takes pop culture seriously, because -- regardless of how ephemeral or unimportant it can seem -- it's a great reflection of what's on people's minds. Johnson talks specifically about Loki's queerness, which is linked to how difficult he can be to pin down: he's not your typical Asgardian (in any incarnation), he's not exclusively bad or exclusively good; he slides past definitions adroitly.

(A sudden thought: given the red hair and general inclination to mischief over evil, I wonder if Good Omens' Crowley, as portrayed by David Tennant, is technically a bit of a variation on Loki himself. In some ways, no, but something of Loki's instinct for self-preservation, adaptability, and unwillingness to be pinned down and defined does ring true for Crowley as well.)

Anyway, it's a slim book and doesn't go into enormous depth, but it's written with a love for Loki and an appreciation for popular culture that I very much enjoyed.