What are specific ways in which pagan and Christian elements are interwoven in Beowulf?
There are components of both pagan and Christian elements in the epic poem Beowulf. Christianity is mentioned within the very first part of the poem, when the narrator is discussing the history of the Danes:
"Shield had a son,/child for his yard, sent by God to comfort the people,to keep them from fear / Grain was his name; / he was famous throughout the North."
Then, a bit later, when Grendel, the villain, is introduced, the narrator states:
"He was of a race of monsters/exiled from mankind by God/He was of the race of Cain,/that man punished for murdering his brother."
Cain and Abel were brothers in the Bible; Caine murdered his brother Abel out of jealousy, thinking that God liked Abel better.
We also see pagan elements in the work, not only in the fighting/warrior society that Beowulf is living in, but also in the idea of fate. In the poem Beowulf states:
"If battle takes me,/send this best of war garments,/this shirt of mail,to Hygelac--/it is an inheritance from Hrethel/and the work of Weland. Fate always goes as it will!"
Beowulf also brags about the fact that FATE was in his own hands when he tells Unferth of his battles with the sea monsters:
"I saw cliffs, the windy/walls of the sea./Fate often saves an undoomed man if his courage holds./Anyway, with my sword/I slew nine sea monsters."
They also speak about the old warrior traditions in pagan society:
"Sometimes a king's man, a warrior/covered in glory who knew/the old traditions, would be/reminded of an ancient song,/and he would call up words adorned/in truth. The man would think/of Beowulf's deeds and quickly/compose a skillful tale in words."
Yet Hrothgar, even though a king and warrior, still speaks of Christianity through God:
"For this sight I give thanks to the Almighty./I have suffered much/from Grendel's scourge./God, the glorious protector,/works wonder after wonder."
So as you can see, pagan and Christian elements run throughout the poem in various parts and through various characters.
This is a great question. If you look at the main themes apart from the biblical quotations, then you will be able to see some of the most important aspects of Christianity and Germanic values. First, there is a strong demarcation between good and evil. Even the imageries of good verse evil is pronounced. Grendel is a monster and Beowulf is far from it. Second, there is a hero, Beowulf who would save his people, even at his own expense. This is the heart of Christianity. Third, everything about the text is about fighting and fighting is tied to a person's worth - a nice window into Germanic culture.