The Dagger in the Desk by Jonathan Stroud

In London, a mysterious and potentially deadly ghost is stalking the halls of St. Simeon’s Academy for Talented Youngsters. It lurks in the shadows, spreading fear and icy cold—and it carries a sharp and very solid dagger… The headmaster wastes no time in enlisting the help of ghost hunters Anthony Lockwood, Lucy Carlyle, and George Cubbins. Can Lockwood & Co. survive the night and save the day?