I'm not into Asatru (I'm just obsessed with Norse mythology and Medieval Scandinavia in general), but on my shelf I've got:
a) A bunch of Sagas.
b) The Prose Edda by Snorri Sturluson (Faulkes translation; I hear it's among the best out there).
c) The Poetic Edda (Larrington translation, same).
d) H. R. Ellis Davidson's "Gods and Myths of Northern Europe" (a classic, superbly-written and very insightful).
e) Else Roesdahl's "The Vikings" (I actually haven't gotten around to reading it yet, but it's highly recommended by John Lindow.
f) The various mythological dictionaries of John Lindow, Rudolf Simek and Andy Orchard. Lindow's is the more accessible (and funny), but Simek and Orchard's version are jam-packed with lots of info.
g) Snorri Sturluson's "Heimskringla" (Lee M. Hollander's translation).
h) Ibn Fadlan's account of his time spent among the "Rus". Michael Chriton (sp?) used this account to write "The Eaters of the Dead", on which the movie "The 13th Warrior" was based.
i) Saxo Grammaticus's History of the Danes (translated by Davidson/Fisher). You'll find the Danish version of the Balder myth in here and lots of other good stuff, although the writing's not the clearest.
j) History of the Archbishops of Hamburg by Adam of Bremen. Haven't read this yet either but he's supposed to give a lot of good geographic/general information on medieval Scandinavia.
k) Beowulf (I have the Seamus Heaney translation).
l) "Runes" by R. I. Page.
m) The Germania by the Roman historian Tacitus. It contains a bunch of info on early Germanic tribes, so it's a bit before true "Viking" times, but it's great nevertheless.
I've also just ordered a hard-to-find copy of "Medieval Scandinavia: An Encyclopedia", edited by Phillip Pulsiano. It's pricy, but I've had a chance to look through a library copy, and I'm sure it's going to be worth it...
Asatru Reading?
