Read the books. As good as the series is, you are not getting the full story or impact with it. There is a lot missing, especially in character development. As an adaption, it's beyond what I hoped it would achieve, it's fantastic in every way. But it isn't the books by a long shot
5 books in the series (so far, 7 planned)! MUCH faster paced than LOTR's, and Martin doesn't take 2-3 pages to describe every mountain range/cave/flower/blade of grass like Tolkien does (I love his style of writing, but still) so you'll probably get through them a lot quicker.
Books 1-3 are just amazing. Book 4 is a bit...well I found it hard going. Book 5 is getting back on track, and i expect book 6/7 to blow all previous books away.