The Book Jumper by Mechtild Gläser

Amy Lennox doesn’t know quite what to expect when she and her mother pick up and leave Germany for Scotland, heading to her mother’s childhood home of Lennox House on the island of Stormsay. 

Amy’s grandmother, Lady Mairead, insists that Amy must read while she resides at Lennox House—but not in the usual way. It turns out that Amy is a book jumper, able to leap into a story and interact with the world inside. As thrilling as Amy’s new power is, it also brings danger: someone is stealing from the books she visits, and that person may be after her life. Teaming up with fellow book jumper Will, Amy vows to get to the bottom of the thefts—at whatever cost.