Game of thrones book 1 to the series?

I recently go into the HBO series, and watched the full season, if i wanted to pick up with where the series left off....

*spoiler*



where the baby dragons are born, would i pick up with book two??? i would really like to keep the story going, and wondered if there was more to book one that the series didn't cover?? or can i move on with the story by reading book 2Game of thrones book 1 to the series?
The show was relatively true to the book as best as possible, however I think you would be missing a lot of the nuances of the story if you did not read the book. You would also miss out on the history of the Seven Kingdoms and the significance of the Stark children's dire wolves.



With that said, A Clash of Kings picks up where Game of Thrones left off and you can probably have no problem following all the plot lines.