Noein is set during a battle between two times: La'cryma, which fights for humanity and Shangri'la, which wants to destroy space-time. The only thing that can stop Shangri'la is something called the Dragon Torque, which a group called the Dragon Cavalry is sent to find. One member, Karasu, discovers a 12-year old girl, Haruka, whom he believes is the Dragon Torque.
Noein Volume 4 picks up the further adventures of Haruka and the rest of the time-traveling crew as they try to save the world in multiple dimensions. Though the ongoing war is very much the center of the show, much of Volume 4 is spent answering questions from previous volumes, most notably Haruka's role as the Dragon Torque. The series also delves into the mysteries surrounding the Dragon Warriors.
Art style is likely the first thing that will pull you into Noein. Though it contains several traits that have come to define what is traditionally labeled as anime, there's a unique artistry behind the series that sets it apart from other shows. The show uses a mix of hand-drawn and CG that blend together really well and grab your attention.
Noein also takes a much different approach with its story. Much of the show's premise is built on the theory that there are series of parallel universes (including our own) created by every possible outcome of a situation. At the same time, it also includes a character, Haruka, who acts as an observer and can decide on the "proper" outcome.
Everything literally wraps into itself throughout the show; an event that takes place in the future may actually be an event taking place in the past and so forth. The complex nature is very cerebral and doesn't dumb anything down - so if you typically don't go for shows that make you think about how elements relate to one another, stay away from Noein.
Even though it is best to begin Noein from the start, you can still go into Noein Volume 4 and enjoy it. Much of what is going on and its significance in the larger scheme of things will be lost on you, but the show is still engaging enough that you will be entertained. It also helps that it answers more questions than it asks, so there is a better feeling of closure.