The Cathedral Museum spreads over four floors and incorporates the cathedral's large 16th-century cloister. You'll see a sizeable section of Maestro Mateo's original carved-stone choir (destroyed in 1604 but pieced back together in 1999), an impressive collection of religious art (including the botafumeiro, the cathedral's famous giant censer, in the 2nd-floor library), the lavish 18th-century sala capitular (chapter house), a room of tapestries woven from designs by Goya, and the Panteón de Reyes, with tombs of kings of medieval León.
Museum tickets are sold at the entrance and on the cathedral website. Combined tickets with the Pórtico de la Gloria will save you a couple of euros.