I highly recommend A Storm of Swords. 
 I am a Stark of Winterfell. Oh yes, I am. 
 I should've learned my lesson from A Game of Thrones, that anything and everything will never be what it seems. 
 A Storm of Swords left me open-mouthed (literally), especially when the Red Wedding took place. There I was, reading leisurely on a Sunday afternoon, when I got the shock of my ASoIaF reading life. So cruel! And yet so grudgingly cunning. 
 New POVs are introduced: Jaime Lannister and Samwell Tarly. I actually enjoyed Jaime's, I mean, who wouldn't want to know what's join on inside the Kingslayer's head? Whatever befell Jaime in ASoS made him change his mind on what the Lannisters are all about. He was running blind, taking orders from who and for what, without asking. But now, ah, Jaime's not as compliant as before, not anymore. Cersei and Tywin were aghast about that. 
 Jon's journey is equally absorbing. The war between the kings seems child's play with what Jon and the brothers of the Night Watch have to face. And those bleak scenes at the Wall, those hopeless actions against the Others and the Wildlings -- a terrific treat to my fantasy appetite. 
 Catelyn's POV are heartbreaking. Such defiance, and ominous pride for a Stark! Arya's plight is getting worse after every chapter. I cannot believe the strength in this skinny girl. Unbelievably daunting. 
 Tyrion. Oh, Tyrion! Dare I say you have the biggest balls amongst the players in the game of thrones? The many, many pages of A Storm of Swords were deduced to nothing, nothing(!) because of the spectacular ending you gave me. *fist pump* 
 Best installment so far. :D Vengeance will soon be ours.