This article is from the Nordic countries FAQ, by Antti Lahelma and Johan Olofsson, with numerous contributions by others.
Although the Vikings were, in theory, a literate people, the runic
script was never used for anything more complicated than a few
sentences, usually commemorating some person or event, e.g "Bjorn had
these runes carved in the memory of Hofdi. He died in Särkland." The
runestones and other archaeological material offer clues as to the
nature of the Norse religion, and there are some accounts by Christian
and Moslem contemporaries of the Vikings -- e.g the bishop of Hamburg,
Adam von Bremen, and the Arab traveler Ibn Fadlan -- but the main
sources of information are the Eddas, written down in Iceland in the
early middle ages. The Poetic Edda is a collection of poems on
mythological themes by anonymous poets; even more important is the
Prose Edda written by the Icelandic scholar Snorri Sturluson in about
1220, which is a collection of old heathen myths in prose form. For
more about sagas and Eddas, see section 5.5. The medieval Danish
historian Saxo Grammaticus can also be mentioned, but he is less
reliable and perhaps less interesting to read.
The problem with those sources is that they were written down hundreds
of years after the conversion of Scandinavians to Christianity, indeed
some of the authors (e.g Saxo) were members of the Catholic clergy,
and their work is to some extent influenced by Christian and classical
ideas. Also, the picture given is no doubt biased towards the
particular form of pagan religion practiced in Iceland; while the main
deities Odin, Thor and Freyr seem to have been worshiped all over
Scandinavia, there must have been a lot of local variation, local
deities, differences in emphasis given to the main deities and their
aspects, etc.
Nevertheless, the stories of the Eddas have become a common cultural
heritage of the Scandinavian countries, and at least a basic knowledge
of it is a must for anybody interested in Scandinavian culture.
The following summary of the main features of Scandinavian mythology
is taken from the excellent book Gods and Myths of Northern Europe, by
H.R.Ellis Davidson, 1964, pages 26-30, Penguin Books.
 
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