A Game of Thrones is the first book in A Song of Ice and Fire, a series of epic fantasy novels by American author George R. R. Martin. It was first published on 6 August 1996. The novel won the 1997 Locus Award, and was nominated for both the 1998 Nebula Award and the 1997 World Fantasy Award. The novella Blood of the Dragon, comprising the Daenerys Targaryen chapters from the novel, won the 1997 Hugo Award for Best Novella. (Wikipedia)
SPOILER!A scene in the first episode includes the discovery of "direwolf" cubs by Lord Eddard Stark, leader of the House Stark. The mother dire wolf had been killed by a stag and the pups are about to be killed as well by the humans who find them. At the last minute, the cubs are saved, adopted by the would be killers, for, as one of the characters says, (paraphrasing) "The wolves were meant for us to find," since the dire wolf is the House Stark's totem.
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I suspect that the fact the bastard of the group found the runt of the litter -- and a white animal -- will reveal something along the lines of this character's heritage. A surprise, a link to royalty (magickal or otherwise), power. The white animal will also become something quite powerful; a protector, a fierce and wise guardian... both outsiders, both carrying power, magick, keepers of a legacy, or secret, a lonely quest, the hero's journey.
For those who know all about Game of Thrones, this might seem obvious, silly, or exasperating ("boy, will she be surprised when it turns out that... ha ha") but for me, it's all new, and I'm looking forward to the rest of the series, including the fate of the direwolves.
Direwolf - Game of Thrones Wiki