The Space Between Worlds
This was a very enjoyable book, sadly let down a little by the choice of formatting in the eBook edition (the line width was artificially narrowed, which made reading it feel more like reading a newspaper than a novel). I've read a few stories inspired by the many-worlds interpretation of quantum mechanics - and even tried to start writing one a few times - including Alastair Reynolds' thought provoking piece Everlasting, but never one in which the protagonist can directly travel to other dimensions. Not as hard sci-fi as some of the others, The Space Between Worlds managed to be a very enjoyable read, while having just enough science and existentialism to get your head working.
Definitely recommended.