Sabriel (Abhorsen Book 1) by Garth Nix
Eighteen year-old Sabriel lives at a boarding school in Ancelstierre, a mundane world reminiscent of England in the early twentieth century. Across the nearby Wall (and garrison that mixes medieval and WWI-era weapons and uniforms) lies the Old Kingdom, place of anarchy and magic where technology will not work.
Sabriel gets a message that something has happened to her father, a famous necromancer. She, a necromancer-in-training, must go into the Old Kingdom and rescue him. On the way, she is helped by a chaotic spirit trapped in the body of a cat, and a prince who has slept for 200 years. Believable magic described in a pure, and pared-down style. Recommended!