Here's how the third volume of Heroes ended, and how the fourth began...
Mohinder/Tracy: Following a battle over the formula - which will be explained in more detaiil below - Mohinder gets covered in the liquid... which successfully reverses the problems he'd been having with his skin and his body. As a result, he walks away from Pinehearst, hoping to start over? And who does he get picked up by on the road?
Tracy, who has been fired by Nathan because she wanted him to give up on the Pinehearst problem due to its PR problem.
Parkman/Daphne/Ando/Hiro: Daphne races to Pinehearst and swipse a vial of the formula. She gives it to Ando, who is intent on becoming a time traveler so he can rescue Hiro. He injects himself with the formula... but no time traveling commences.
Instead, it appears as though Ando's ability is to charge the abilities of others. When Parkman touches him, he can hear everyone's thoughts in the city. Therefore, an idae is formed: if Daphne races around, while touching Ando, she can run faster than the speed of light and actually travel back in time. This experiment is attemped, and it works. Daphne and Ando sprint back 16 years and grab Hiro from his past.
In the present, Hiro and Daphne then race to Pinehearst, grab the two pieces of paper that make up the formula and destroy them.
HRG/Angela/Claire/Meredith/Sylar: Now that he's officially a monster again, Sylar travels t Primatech with one goal in mind: revenge. He traps the aforementioned quartet of characters inside the facility and aims to prove that each is a villain. He then stabs Meredith in the heart with adrenaline, causing her to be overly flammable and unable to control her ability. From there, he finds himself alone with Angela and presses her about his heritage. Angela claims she knows who Sylar's real parents are.
But does she reveal this information? And does either even make it out of Primatech alive? We'll need to wait until volume four to find out because Claire stabs Sylar in the back of the head, supposedly rendering him powerless. Immediately after she does, HRG grabs his daughter and the two of them sprint out of the building just as it blows up, due to Meredith's out-of-control ability. Claire's biological mother is definitely dead, as is Angela, we presume.
Peter/Nathan: These brothers just can't get alone. Peter is intent in destroying every last vial of the formula, as he actually gets help from Knox and Flint (because they wish to remain special) as he does so. Once Flint sets fire to the Pinehearst lab, Peter sees only one way to save himself and Nathan: he injects himself with the formula (sort of proving Nathan's point that this formula can be be used for heroic purposes), grabs Nathan before the building blows up and flies them to safety.
Once the pair lands, though, Nathan goes off on his brother. He simply says that he wouldn't have done what Peter just did (even though, well, didn't Nathan do this exact thing when he flew Peter into outer space at the conclusion of season one?). Nathan flies off and we're taken to a scene that sets the stage for Volume Four:
Nathan is sitting in a limo, three weeks later, with the President of the United States. He receives permission for his mission, which is this: to round up everyone with abilities and store them someplace where they can do no harm. Fade to black...