Green Lantern: Emerald Twilight/A New Dawn (TPB collects Green Lantern Vol. 3 #48-55)- This trade features Hal Jordan's fall, the destruction of the Green Lantern Corps, and Kyle Rayner's first adventures as Green Lantern.
Green Lantern (Vol. 3) #0- This single issue features a confrontation between the apparently crazy Hal Jordan and new GL Kyle Rayner. I don't know if this is in any TPBs or not, but it is an amazing issue, definitively crowning Kyle Rayner as the new GL.
Green Lantern: New Journey, Old Path (TPB that collects Green Lantern Vol. 3 #129-136): This collection features Kyle Rayner going up against a mad man name Nero who has a yellow power ring. Nero is one of the toughest opponents Kyle ever faced during his time as the only GL.
Green Lantern: The Power of Ion (TPB that collects Green Lantern Vol. 3 #142-150): In this collection, Kyle Rayner gains god-like powers after another confrontation with Nero. This story is about how Kyle uses his powers and what he ultimately decides he should do with them.
Green Lantern: New Guardians: The Ring Bearer (TPB that collects Green Lantern: New Guardians #1-7)- This trade collects the first story arc of Kyle's own series in the New 52. Rings from several different Lantern Corps are leaving their owners in order to come to Kyle, who has no idea why this is happening. Members of the other corps are none to happy about it either. Kyle and this motley group of representatives from each of the different lantern corps aim to get to the bottom of this mystery.