Warning: this does contain spoilers.
1. Yara Greyjoy
In the show, Theon Greyjoy's sister Yara is a tough woman who knows she is a great leader and is willing to go to any measures to prove herself. In the books all of that is true. Oh, except for the part where her name is Asha, not Yara.
2. Lady Stoneheart
Catelyn Stark is pretty much the ultimate mother who will go to any lengths to protect her children in both the show and the books. However in the books, after Catelyn Stark is murdered, she is brought back to life as a half-dead woman called Lady Stoneheart who hangs the men that terrorized her family.
3. Sansa & Ramsay Bolton
In the show, Sansa Stark is married to Ramsay Bolton and pretty much suffers through the worst marriage in the series. In the books however, Ramsay marries Sansa's old friend Jayne Poole who is pretending to be Arya Stark.
4. Mance Rayder
In the show, Mance Rayder is burned at the stake by the order of Stannis Baratheon. In the books, Mance has been disguised as Rattleshirt (another wildling) by the Red Woman's magic and is sent off by Jon Snow to find Arya Stark.
5. Robb Stark's marriage
In the show, Robb Stark marries a woman named Lady Talisa, who he then impregnates and who is murdered at the infamous Red Wedding. But in the books, Robb marries a woman named Jeyne Westerling whom he was not able to impregnate and who was not present at the Red Wedding.
6. Character's ages
It may surprise people that in the books, the children, and even the characters that aren't thought of as children (Daenerys, Jon) are much younger than in the show. When Daenerys is married to Khal Drogo, she is only 13. When Jon Snow leaves for the wall, he is 14. Tommen Baratheon was only six when the books started.
7. The Hound and Brienne
In the books, Brienne and the Hound never cross paths, and they certainly never fight the huge battle that ensues in the show. Instead, Arya leaves the Hound to die from an infection.
8. Aegon Targaryen
In the show, Tyrion Lannister never encounters any memorable characters on his way to find Daenerys Targaryen. But in the books, he meets a young man who is journeying to Westeros. This man eventually turns out to be Aegon Targaryen, the supposedly murdered son of Rhaegar Targaryen.
This is minor, but in the books, Daenerys' confidant and translator Missandei is only 10, whereas in the show she is much older.
10. Jon Stark?
In the books, before Robb Stark dies, he legitimizes Jon Snow. This means that Robb makes Jon Snow a legitimate son of Ned Stark and the next heir to Winterfell (if he hadn't taken the black). This never happens in the show.
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