What happened between Halo 3 and Halo 4?

I just got Halo 4 yesterday. I am playing through the campaign, but I am a little confused. It seems like a lot has changed since the end of Halo 3. I assume there are books that explain everything, but if I don't want to read those. Can someone please give a brief explanation of what happened in those 4.5 years?

At the end of Halo 3, Master Chief is drifting through space in the back half of the Forward Unto Dawn. Cortana is nearing the end of her useful life cycle and is beginning to become rampant. However, she decides to put Master Chief into stasis, send out a distress signal, and remain active to monitor the situation.

Time passes. There are a lot of political and social upheavals within the Covenant as a result of the Human-Covenant war that came to a head in Halo 3. While some of the Sangheili believe that allying with the humans is the correct course of action, there are more than a few rebels who believe the humans are still an enemy. Much of this is contained in novels, rather than plot in-game.

Eventually, the distress signal from Forward Unto Dawn is received by the UNSC, and they dispatch the UNSC Infinity to rescue Master Chief. (The arc that leads to this is the live-action series Forward Unto Dawn).

The Forward Unto Dawn is falling towards Forerunner Shield World called Requiem which was designed as a military base by the Forerunners, and is supposed to be a safe haven from the Flood. If you finish Halo 3 on Legendary, you get a short glimpse of this world as part of the end cutscene.

Meanwhile, a group of anti-human Covenant called the Remnant has also found Requiem and is attempting to breach it, seeking to steal the Forerunner technology inside as a means to eradicate the humans. These Covenant and their leader are featured prominently in the Spartan Ops campaign in Halo 4.

What's actually inside is a powerful Forerunner "general" of sorts who was imprisoned for various complex reasons which you can read about in his article here. He's got kind of a grudge against humans, and isn't above sacrificing them for his own ends. Needless to say, the guy gets along with the Covenant Remnant pretty well, and this "dream team" of Covenant, the Didact, and the Didact's army of Prometheans form the primary antagonists of Halo 4.