This was the source of power for the frost giants from the realm of Jotunheim. Odin took it after defeating them and kept it in the palace in Asgard. Loki later took it and it seems to have been lost when the bifrost was destroyed. If you watch the film, you may think that there are no letters shown here; but if you lighten the frame, you can see that the pedestal has runes carved into it. The runes are like a museum label, telling you what this item is.
Book of Yggdrasil
This manuscript tells about the source of power for the dark elves from the realm of Svartalfheim. Odin shows it to Thor and Jane when he tells them about the aether. At least five pages are shown in the film, some more than others. This is the page that is viewed the longest and where we see the fullest text.
"The elves fought the light that radiated from Asgard. They built a weapon out of the darkness and unleashed the dark power of the Aether across the nine realms, inflicting the torment of war."
Note that the word "aether" has a reddish cast. I think that was intentional, as the aether is red. The following is a page that's briefly shown. We can piece together the missing text from supplemental photos of the movie props (link).
"The birth of the nine realms. From out of the cold darkness of the universe came forth the first dawn of light. Born out of a spark of golden energy the ethereal light filled the far reaches of the universe."
This final image is actually the first view that we get of this book. This seems to be the title page. As the page is turned, we get a glimpse of the top of the first page where it reads in runes: "the dark elves". However, the main portion of the page is filled with some other form of writing - it looks like a type of cursive script. Asgardian script, perhaps? I haven't been able to determine whether the letters are real or invented. So the meaning remains a mystery. I've tried reaching out to various sources and blogs to get more information and will add updates if I hear from them.
So far, those are the only writings in Asgard that I've been able to spot. Have I missed any? I have a feeling there may be others hidden among the rooms, books, and props designed for the movies. I wish that I could catch a glimpse inside one of the books that Frigga gave to Loki. According to an interview that I saw, his mother gave him some "edifying" books. Good idea^^