a song of ice and fire - Which book and chapter match with episode 8 season 3 from Game of Thrones TV Series?

I would offer to say that you not jump ahead. Sure the major events are more or less the same in the book and the series, but they are not identical. Also, the books are far more nuanced and character rich than the TV series is. If you do jump ahead you'll find yourself more confused than relieved. Just off the top of my head you'll start wondering who the heck Asha is, or Jeyne Westerling, or Strong Belwas ... etc. You'll find yourself slogging through a several dozen new characters (or characterizations) just to get by. It's doable with a bit of Googling, but I really do advise you to read the books from the beginning. You'll get a much better understanding of the history of Westeros that led to the current crisis, and a deeper outlook into the motivations of the characters.

Edited to add, there are several extremely interesting and cool scenes that had to be cut out of the TV series due to budget or time constraints. The famous Tower of Joy comes to mind. If you skip the books you miss out on some very important events that get mentioned later on.