Knights and Knaves Puzzle

There are three people (Alex, Brook and Cody), one of whom is a knight, one a knave, and one a spy.

The knight always tells the truth, the knave always lies, and the spy can either lie or tell the truth.

Alex says: "Cody is a knave."
Brook says: "Alex is a knight."
Cody says: "I am the spy."

Who is the knight, who the knave, and who the spy?