Actually I think you read parts 2 and 3, A Game of Thrones is number 1. And as far as I know, Martin is still working on book 4, and has been for a while. His books are long, so it will take a while... I'm pretty sure theres a book 5 off in the distant future somewhere. A [something] with Wolves and a [something] with Dragons, I'm not sure which will be 4 and which will be 5.