The first one I would start with is Mircea Eliade's "The Myth of the Eternal Return: Cosmos and History"
http://www.amazon.com/Myth-Eternal-R...eternal+return
It's, in my opinion, absolutely essential reading for average 'Westerners' to be able to start to understand that for non-Abrahamic cultures, historical and mythological time wasn't combined together. This plays into the way that polytheistic cultures interacted with their gods, spirits, ancestors, etc. as it explains how
mythologically cosmogonic, eschatological (and all in-between) processes are constantly ongoing and can be culturally interacted with via communal or individual ritual.
The 'paradigm shift' of thought that Eliade provides is essential to even attempting to understand how polytheistic cultures would have seen the world, their gods, their rituals, and each other.
His book "Myth and Reality" then expands upon the groundwork laid in "Eternal Return."
http://www.amazon.com/Myth-Reality-R...yth+as+reality
I would also recommend Scott Littleton's (editor) "The New Comparative Mythology"
http://www.amazon.com/New-Comparativ...tive+mythology
These are a series of essays analyzing aspects of the Dumezelian approach to (specifically) Indo-European cultures. If I'm remembering right, a few of them go in to the evolving academic thought behind what 'gods' are to a people (euhumerized ancestors, explanations of nature, to the more nuanced view mentioned above in this thread).
Then there is Georges Dumezil's work itself. A lot of his 'conclusions' are debated, questioned, championed, etc. depending on political and geographical factors but his work is such that it can't be ignored.
"Gods of the Ancient Northmen"
http://www.amazon.com/Northmen-Compa...eorges+dumezil
While sounding Norse specific, actually lays out much of the groundwork for his analyses of Norse, Greek, Roman, Vedic, Hindu, and Iranian mythology and social structure (and how the two are interwoven).
Also his "The Destiny of the Warrior" and "The Destiny of a King" both go into the cultural roles of those classes, how they interact with the gods that provide exemplary models for each and, pertinent here, demonstrate a bit of how gods like Ares or Zeus would have been seen by the cultures that worshipped them.
His "Archaic Roman Religion" vols 1 and 2 are excellent also.
That should more than get you started.

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