Best way to boil down this story would be to say it's a romance (YA-ish... it gets pretty R rated sometomes) meets Schrodinger's cat meets that 90's TV show "Sliders." 
 It was an interesting concept to have the character moving between dimensions and inhabiting new worlds and lives. However, it does bring up the moral/ethical issue of "inhabiting" another person. Essentially they are hijacking the consciousness of their other selves in different dimensions. The version of them there just fades into the background. (view spoiler)[However, the current versions are somewhat aware of the the other version is doing in their body, like twilight sleep. (hide spoiler)] 
 O and RUSSIA. The rest of this will be blocked for spoilers. (view spoiler)[There is a lot of controversy of the sex scene between Marguerite and Paul. I understand that she fell in love with the Paul in that dimension and when she had sex with him, she was acting on that love. The scene would have been a beautiful moment between the two IF SHE WAS IN HER OWN BODY AT THE TIME! It's kinda like she raped herself by proxy and deceived Paul because he thought he was with his Marguerite. So basically I'm really rather conflicted about the scene. (hide spoiler)] 
 The science was a little hokey. Basically a magic necklace allows you to go to other dimensions and also does a bunch of other stuff. Its able to work because reasons... Yes, I do see the irony in pointing out that the science was unbelievable in a "science-fiction" novel. I bought into the mythos and went along with it. Just wanted there to be some more concreate reasoning besides "It works cause I say so." 
 I really didn't see all the twists coming at the end. Overall, it was a pretty good book. Not amazing, but pretty good.